1. The girl sitting on a swing stands up. What will be the effect on periodic time of swing?
2. At what distance from the mean position, is the kinetic energy in a simple harmonic oscillator equal to potential energy?
3. A simple harmonic oscillator is represented by the equation :
Y = 0.40 Sin(440t+0.61), Where Y is in metres t is in seconds
Find the values of 1) Amplitude 2) Angular frequency 3) Frequency of oscillation 4) Time period of oscillation, 5) Initial phase.
4. The soldiers marching on a suspended bridge are advised to go out of steps. Why? [1]
5. The springs of spring factor k, 2k, k respectively are connected in parallel to a mass m. If the mass = 0.08 kg-m and k = 2N/m, then find the new time period?
6. The bob of a vibrating simple pendulum is made of ice. How will the period of swing will change when the ice starts melting?
7. An 8 kg body performs S.H.M. of amplitude 30 cm. The restoring force is 60N, when the displacement is 30cm. Find: – a) Time period b) the acceleration c) potential and kinetic energy when the displacement is 12cm?
8. What is Simple pendulum? Find an expression for the time period and frequency of a simple pendulum?
9. A particle executing SH.M has a maximum displacement of 4 cm and its acceleration at a distance of 1 cm from its mean position is 3 cm/s^2. What will be its velocity when it is at a distance of 2 cm from its mean position?
10. What is ratio of frequencies of the vertical oscillations when two springs of spring constant K are connected in series and then in parallel? [2]
11. The kinetic energy of a particle executing S.H.M. is 16J when it is in its mean position. If the amplitude of oscillations is 25cm and the mass of the particle is 5.12kg. Calculate the time period of oscillations?
12. Is the motion of a simple pendulum strictly simple harmonic? [1]
13. Can a simple pendulum experiment be done inside a satellite? [1]
14. Give some practical examples of S. H. M? [1]
15. The time period of a body suspended by a spring is T. What will be the new time period if the spring is cut into two equal parts and
(A) the body is suspended by one part.
(B) Suspended by both parts in parallel? [2]
16. A simple pendulum is executing Simple harmonic motion with a time T. If the length of the pendulum is increased by 21 %. Find the increase in its time period? [2]
17. A particle is executing S H M of amplitude 4 cm and T = 4 sec. find the time taken by it to move from positive extreme position to half of its amplitude? [2]
18. Two linear simple harmonic motions of equal amplitudes and angular frequency w and 2 w are impressed on a particle along axis X and Y respectively. If the initial phase difference between them is π/2, find the resultant path followed by the particle? [2]
19. The acceleration due to gravity on the surface of moon is 1.7 m/s^2. What is the time period of simple pendulum on moon if its time period on the earth is 3.5 s? [2]
20. Using the correspondence of S. H. M. and uniform circular motion, find displacement, velocity, amplitude, time period and frequency of a particle executing SH.M? [2]
