Simple Harmonic Motion PYQs Set 11 (PDF)

Set 11 of 13 · Questions 301-330 of 372

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Mere Teacher · Previous Year Questions JEE Main Physics · Simple Harmonic Motion · Set 11 (Q301-330)
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301. $A particle executes SHM of type x = Asin ωt . It takes time t_{1} from x = 0 to x = \frac{A}{2} and t_{2} from x = \frac{A}{2} to x = A . The ratio t_{1} : t_{2} will be$ (1) $1 : 1$ (2) $1 : 2$ (3) $1 : 3$ (4) $2 : 1$ 302. $A particle oscillates along the x -axis according to the law, x (t) = x_{0} sin^{2} (\frac{t}{2}) where x_{0} 1 m . The kinetic energy (K) of the particle as a function of x is correctly represented by the graph$ (1) (2) (3) (4) 303. $A simple pendulum of length L is placed between the plates of a parallel plate capacitor having electric field E, as shown in figure. Its bob has mass m and charge q . The time period of the pendulum is given by:$ (1) $2 π \frac{L}{( g + \frac{qE}{m} )}$ (2) $2 π \frac{L}{g ^{2} - \frac{q ^{2} E ^{2}}{m ^{2}}}$ (3) $2 π \frac{L}{( g - \frac{qE}{m} )}$ (4) $2 π \frac{L}{g ^{2} + ( \frac{qE}{m} ) ^{2}}$ 304. $A simple pendulum consists of a small sphere of mass 'm' suspended by a thread of length 'l'. The sphere carries a positive charge q . The pendulum is allowed to do small oscillations in a uniform electric field E with direction vertically upwards. The time period of oscillation is$ (1) $2 π \frac{l}{g}$ (2) $2 π \frac{ml}{qE}$ (3) $2 π \frac{l}{g - \frac{q}{m} E}$ (4) $2 π \frac{l}{g + \frac{q}{m} E}$ 305. $In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support.The spring constant of the spring is k . The mass oscillates on a frictionless surface with time period T andamplitude A . When the mass is in equilibrium position, as shown in the figure, another mass m is gently fixedupon it. The new amplitude of oscillation will be -$ (1) $A \frac{M}{M + m}$ (2) $A \frac{M}{M - m}$ (3) $A \frac{M - m}{M}$ (4) $A \frac{M + m}{M}$ 306. $Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance R /2 from the earth'scenter, where ’ R ’ is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in thistunnel, it will execute a simple harmonic motion with a time period:$ (1) $2 π \frac{R}{g}$ (2) $\frac{1}{2 π} \frac{g}{R}$ (3) $\frac{2 πR}{g}$ (4) $\frac{g}{2 πR}$ 307. $A particle executes simple harmonic motion between x = -A and x = +A. If time taken by particle to go from x = 0 to \frac{A}{2} is 2s; then time A taken by particle in going from x= \frac{A}{2} to A is:$ (1) $3s$ (2) $2s$ (3) $1.5s$ (4) $4s$ 308. $The x -t graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at t = 2 s is [NEET 2023]$ (1) $- \frac{π ^{2}}{8} ms^{- 2}$ (2) $\frac{π ^{2}}{16} ms^{- 2}$ (3) $- \frac{π ^{2}}{16} ms^{- 2}$ (4) $\frac{π ^{2}}{8} ms^{- 2}$ 309. $9 kg . solution is poured into a glass U-tube as shown in the figure below. The tube's inner diameter is 2 \frac{π}{5} m and the solution oscillates freely up and down about its position of equilibrium (x = 0) . The period of oscillation in seconds is (1 m^{3}) of solution has a mass μ = 900 kg, g = 10 m / s^{2}, ignore frictional and surface tension effects)$ (1) $0.1$ (2) $10$ (3) $π$ (4) $1$ 310. $A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle (θ) of thread deflection in the extreme position will be:$ (1) $tan^{- 1} (2)$ (2) $2 tan^{- 1} (\frac{1}{2})$ (3) $tan^{- 1} (\frac{1}{2})$ (4) $2 tan^{- 1} (\frac{1}{5})$ 311. $A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is 200 N / m . The block is pushed such that the length of the spring becomes 1 m and then released. At distance x m (x < 2) from the wall, the speed of the block will be$ (1) $10 (1 - (2 - x)^{2})^{\frac{1}{2}} m / s$ (2) $10 (1 - (2 - x)^{2})^{\frac{3}{2}} m / s$ (3) $10 (1 - (2 - x)^{2}) m / s$ (4) $10 (1 - (2 - x)^{2})^{2} m / s$ 312. $Which one of the following statements is true for the speed v and the acceleration a of a particle executing simple harmonic motion?$ (1) $When v is maximum, a is maximum.$ (2) $Value of a is zero, whatever may be the value of v .$ (3) $When v is zero, a is zero.$ (4) $When v is maximum, a is zero.$ 313. $Displacement between maximum potential energy position and maximum kinetic energy position for a particle executing simple harmonic motion is$ (1) $\pm a /2$ (2) $+ a$ (3) $\pm a$ (4) $- 1 .$ 314. $The period of oscillation of a mass A4 suspended from a spring of negligible mass is T . If along with it another mass M is also suspended, the period of oscillation will now be$ (1) $T$ (2) $\frac{T}{2}$ (3) $2 T$ (4) $2 τ$ 315. $A simple pendulum performs simple harmonic motion about x = 0 with an amplitude a and time period T . The speed of the pendulum at x = a /2 will be$ (1) $\frac{πa}{T}$ (2) $\frac{3 π ^{2} a}{T}$ (3) $\frac{πa 3}{T}$ (4) $\frac{πa 3}{2 T}$ 316. $A vertical spring mass system has the same time period as simple pendulum undergoing small oscillations. Now, both of them are put in an elevator going downwards with an acceleration 5 m / s^{2} . The ratio of time period of the spring mass system to the time period of the pendulum is (Assume, acceleration due to gravity, = 10 m / s^{2})$ (1) $\frac{3}{2}$ (2) $\frac{2}{3}$ (3) $\frac{1}{2}$ (4) $2$ 317. $A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3 s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5 s. The value of m in kg is:$ (1) $\frac{9}{16}$ (2) $\frac{3}{4}$ (3) $\frac{4}{3}$ (4) $\frac{16}{9}$ 318. $The mass M shown in the figure oscillates in simple harmonic motion with amplitude A . The amplitude of point P is$ (1) $\frac{k _{1} A}{k _{2}}$ (2) $\frac{k _{2} A}{k _{1}}$ (3) $\frac{k _{1} A}{k _{1} + k _{2}}$ (4) $\frac{k _{2} A}{k _{1} + k _{2}}$ 319. $A mass of 5kg is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length 4m has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed?$ (1) $10m/ s^{2}$ (2) $5m/ s^{2}$ (3) $4 m/ s^{2}$ (4) $9.8 m/ s^{2}$ 320. $A particle is executing simple harmonic motion with time period 2 s and amplitude 1 cm. If D and d are the total distance and displacement covered by the particle in 12.5 s, then \frac{D}{d} is$ (1) $\frac{16}{5}$ (2) $10$ (3) $\frac{15}{4}$ (4) $25$ 321. $A particle starts with S.H.M. from the mean position as shown in the figure. Its amplitude is A and its time period is T . At one time, its speed is half that of the maximum speed. What is this displacement?$ (1) $\frac{2 A}{3}$ (2) $\frac{3 A}{2}$ (3) $\frac{2 A}{3}$ (4) $\frac{3 A}{2} .$ 322. $A particle of mass m is attached to one end of a mass-less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0 with an initial velocity u_{0} . When the speed of the particle is 0.5 u_{0}, it collies elastically with a rigid wall. After this collision:$ (1) $the speed of the particle when it returns to its equilibrium position is u_{0} .$ (2) $the time at which the particle passes through the equilibrium position for the first time is t = π \frac{m}{k} .$ (3) $the time at which the maximum compression of the spring occurs is t = \frac{4 π}{3} \frac{m}{k} .$ (4) $the time at which the particle passes throughout the equilibrium position for the second time is t = \frac{5 π}{3} \frac{m}{k} .$ 323. $The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the below figure. [NEET 2019] y -projection of the radius vector of rotating particle P is$ (1) $y (t) = 4 sin (\frac{πt}{2}), where y in m$ (2) $y (t) = 3 cos (\frac{3 πt}{2}), where y in m$ (3) $y (t) = 3 cos (\frac{πt}{2}), where y in m$ (4) $y (t) = - 3 cos 2 πt, where y in m$ 324. $A body of mass 200g is tied to a spring of spring constant 12.5 N/m, while the other end of spring is fixed at point O. If the body moves about O in a circular path on a smooth horizontal surface with constant angular speed 5 rad/s, then the ratio of extension in the spring to its natural length will be:$ (1) $1:2$ (2) $1:1$ (3) $2:3$ (4) $2:5$ 325. $Two identical spring of spring constant ’ 2 K ’ are attached to a block of mass m and to fixed support (seefigure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. Then time period of oscillations of this system is:$ (1) $π \frac{m}{k}$ (2) $π \frac{m}{2 k}$ (3) $2 π \frac{m}{k}$ (4) $2 π \frac{m}{2 k}$ 326. $A light hollow cube of side length 10 cm and mass 10 g, is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is yπ \times 10^{- 2} s, where the value of y is (Acceleration due to gravity, g = 10 m / s^{2}, density of water = 10^{3} kg / m^{3})$ (1) $6$ (2) $2$ (3) $4$ (4) $1$ 327. $A simple harmonic oscillator has an amplitude A and time period 6 π second. Assuming the oscillation starts from its mean position, the time required by it to travel from x = A to x = \frac{3}{2} A will be \frac{π}{x} s, where x =______$ 328. $Consider two identical springs each of spring constant k and negligible mass compared to the mass M asshown. Fig. 1 shows one of them and Fig. 2 shows their series combination. The ratios of time period ofoscillation of the two SHM is \frac{T _{b}}{T _{a}} = x, where value of x is_____(Round off to the Nearest Integer)$ 329. $In the figure given below, a block of mass M = 490 g placed on a frictionless table is connected with two springs having same spring constant (K= 2 N m^{- 1}). If the block is horizontally displaced through 'X'm then the number of complete oscillations it will make in 14n seconds will be________$ 330. $A block of mass 2 kg is attached with two identical springs of spring constant 20 N/m each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is \frac{π}{x} in SI unit. The value of x is____________.$