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SIMPLE HARMONIC MOTION
 1. An object oscillates with s.h.m. of time period 4s. a) Calculate the magnitude of the constant which relates the acceleration of the object to its displacement b) Calculate the acceleration when the displacement is 2×10-2m. 2. During a simple harmonic oscillation, the acceleration is 4cms-2 when the displacement is 5cm. Calculate the time period. 3. A point is moving with s.h.m. of time period 10s and amplitude 15cm. At t=0 the displacement is 0. Calculate the displacement at t=2s 4. A body is moving with s.h.m. of time period 0.2s and amplitude 1cm. At t=0 the body is at its equilibrium position. a) Calculate the first time (after t=0) at which the mass will be 0.5cm from its equilibrium position b) Calculate the next time at which it will have the same displacement. 5. A body is moving with s.h.m. of time period 5s and amplitude 0.4m. At t=0 the body is at its equilibrium position. a) Calculate the maximum speed of the object b) Calculate the speed at time t=2s. c) At t=2s, is the object moving towards or away from the equilibrium position? 6. A body oscillates with s.h.m. with a frequency of 100Hz. At t=0 it is at the equilibrium position. What is speed of the body at t=2.5×10-3s? 7. An object of mass 0.5kg moves with s.h.m. of time period 1.5s and amplitude 5×10-3m. a) Calculate the value of the constant k (the force per unit displacement) for this motion b) Calculate the restoring maximum force which acts on the mass (assume there are no other forces acting on it). 8. Describe (briefly) the energy changes which take place when a) a pendulum oscillates in air b) a mass oscillates (vertically) on a spring, in a vacuum. 9. On the earth, a pendulum has a time period of 1.5s and a mass/spring oscillator has a time period 0.8s. If both these objects were taken to the moon, what would their time periods be? Take the acceleration due to gravity on the moon to be g/6 10. A pendulum has a bob of mass 0.2kg. It has a length of 0.5m. Ignoring the effects of air resistance, calculate a) the maximum kinetic energy of the bob given that the initial displacement from the equilibrium position is 0.2m b) the total energy of this oscillation.

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