Chapter Test: SHM- 1 - JEE MCQ

A simple pendulum 4 m long swings with an amplitude of 0.2 m. What is its acceleration at the ends of its path ? 

(g = 10 m/s²)

In the figure shown a massless spring of stiffness 100 N/m and natural length l₀ m is rigidly attached to a block of mass 20 kg and is in vertical position. A wooden ball of mass m is released from rest to fall under gravity. Having fallen through a height h the ball strikes the spring and gets stuck up in the spring at the top. What should be the minimum value of h (in cm) so that the lower block will just lose contact with the ground later on? Neglect any loss of energy.

A body is executing SHM. When the displacement from the mean position is 4cm and 5 cm. The values of the corresponding velocity of the body are 10 cm s^–1 and 8 cm s^–1. Then the time period of the body is -

A particle at the end of a spring executes simple harmonic motion with a period t₁, while the corresponding period for another spring is t₂. If the period of oscillation with the two springs in series is T, then -

A particle performs harmonic oscillations along a straight line with a period T and amplitude a. The mean velocity of the particle averaged over the time interval during which it travels a distance a/2 starting from the extreme position is :

Particle moves on the x-axis according to the equation x = A + B sin ωt. The motion is simple harmonic with amplitude.

A system is shown in the figure. The time period for small oscillations of the two blocks will be -

The acceleration-displacement (a-x) graph of a particle executing simple motion is shown in figure. The frequency of oscillation is given by -

A particle is vibrating in simple harmonic motion with an amplitude of 4 cm. At what displacement from the equilibrium position is its energy half potential and half kinetic ?

A pendulum of length 200 cm is horizontal when its bob of mass 200 gm is released. It has 90% of initial energy when the bob reaches the lower most point. Speed of the bob at this point is -

A simple pendulum with angular frequency ω oscillates simple harmonically. The tension in the string at lowest point is T. The total acceleration of the bob at its lowest position is -

A second pendulum is mounted in a space shuttle. Its period of oscillations will decrease when rocket is:

A particle of mass 10 gm lies in a potential field v = (50x²+100) J/kg. The value of frequency of oscillations in cycle/sec is

Find the amplitude of the S.H.M whose displacement y in cm is given by equation y= 3 sin157t + 4 cos157t, where t is time in seconds.

A particle executes linear simple harmonic motion with an amplitude of 2 cm. When the particle is at 1 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is:

A uniform solid cylinder of mass 5 kg and radius 0.1 m is resting on a horizontal platform (parallel to the x-y plane) and is free to rotate about its axis along the y-axis. The platform is given a motion in the x direction given by x = 0.2 cos(10t) m. If there is no slipping, then maximum torque acting on the cylinder during its motion is

A short boy sits on a seat suspended by a light string from a fixed point O and starts swinging in a vertical plane from the extreme position P with a small amplitude. The graph, which shows the variation of the tension in the string with time ‘t’ is :

Two small bobs of same mass are hung from two threads of different length as shown. The bobs are just touching each other. Now the left bob is pulled out by a small angle (θ < 10°)="" in="" same="" vertical="" plane="" and="" released="" at="" t="0." it="" collides="" with="" the="" other="" bob.="" at="" what="" time(s)="" the="" two="" bobs="" do="" not="" collide="" with="" each="" />

A body is executing SHM. When the displacement from the mean position is 4cm and 5 cm. The values of the corresponding velocity of the body are 10 cm s^–1 and 8 cm s^–1. Then the time period of the body is -

A hollow sphere is filled with water. It is hung by a long thread to make it a simple pendulum. As the water flows out of a hole at the bottom of the sphere, the frequency of oscillation will

A block is resting on a piston which executes simple harmonic motion in vertical plain with a period of 2.0 s in vertical plane at an amplitude just sufficient for the block to separate from the piston. The maximum velocity of the piston is

The displacement x (in meter) of a particle performing simple harmonic motion is related to time t (in second) as x = 0.05cos(4πt+π/4).The frequency of the motion will be

Figure shows the variation of force acting on a particle of mass 400 g executing simple harmonic motion. The frequency of oscillation of the particle is