CBSE Class 12 Physics Simple Harmonic Motion Basic Problems

CBSE Class 12 Physics Simple Harmonic Motion Basic Problems. Please refer to the examination notes which you can use for preparing and revising for exams. These notes will help you to revise the concepts quickly and get good marks.

1. Consider a particle moving in simple harmonic motion according to the equation x = 2.0 cos (50 πt + tan^–1 0.75) where x is in centimeter and t in second. The motion is started at t = 0.
(a) When does the particle come to rest for the first time?
(b) When does the acceleration have its maximum magnitude for the first time?
(c) When does the particle come to rest for the second time?

2. The equation of motion of a particle started at t = 0 is given by x = 5 sin (20 t + π/3) where x is in centimetre and t in second. When does the particle
(a) first come to rest
(b) first have zero acceleration
(c) first have maximum speed?

3. A particle having mass 10 g oscillates according to the equation x = (2.0) sin[(100)t + π/6] where x is in cm and t is in sec. Find
(a) the amplitude, the time period and the spring constant
(b) the position, the velocity and the acceleration at t = 0

4. A small block of mass m is kept on a bigger block of mass M which is attached to a vertical spring of spring constant k as shown in the figure. The system oscillates vertically.
(a) Find the resultant force on the smaller block when it is displaced through a distance x above its equilibrium position.

(b) Find the normal force on the smaller block at this position. When is this force smallest in magnitude?
(c) What can be the maximum amplitude with which the two blocks may oscillate together?

5. The block of mass m1 shown in figure is fastened to the spring and the block of mass m2 is placed against it

(a) Find the compression of the spring in the equilibrium position
(b) The blocks are pushed a further distance (2/k) (m₁+ m₂)g sin θ against the spring and released. Find the position where the two blocks separate.
(c) What is the common speed of blocks at the time of separation?

6. The spring shown in figure is unstretched when a man starts pulling the block. The mass of the block is M. If the man exerts a constant force F, find

(a) the amplitude and the time period of the motion of the block,
(b) the energy stored in the spring when the block passes through the equilibrium position and
(c) the kinetic energy of the block at equilibrium position.
7. A particle of mass m is attached to three springs A, B and C of equal force constants k as shown in figure. If the particle is pushed slightly against the spring C and released, find the time period of oscillation.

8. The string, the spring and the pulley shown in figure are light. Find the time period of the mass m if it is displaced slightly from equilibrium position

9. Solve the previous problem if the pulley has a moment of inertia I about its axis and the string does not slip over it.

10. A 1 kg block is executing simple harmonic motion of amplitude 0.1 m on a smooth horizontal surface under the restoring force of a spring of spring constant 100 N/m. A block of mass 3 kg is gently placed on it at the instant it passes through the mean position. Assuming that the two blocks move together, find the frequency and the amplitude of the motion.

11. The left block in figure moves at a speed v towards the right block placed in equilibrium. All collisions to take place are elastic and the surfaces are frictionless. Show that the motions of the two blocks are periodic. Find the time period of these periodic motions. Neglect the widths of the blocks.

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