1 The motion
of a mass m is represented by the following expressions, where x is the
displacement from a fixed point and k and a are positive constants. Which of
these expressions represent simple harmonic motion?
A acceleration = kx, B velocity = kx, C acceleration = -kx
D velocity = -k(x2 - a2), E
velocity = k(a2 x) A acceleration = kx, B velocity = kx, C acceleration = -kx
2 A mass of 0.01 kg is vibrating up and down with simple harmonic motion; its amplitude is 40mm, and the period is 2s. Find (i) the velocity and acceleration at the centre of oscillation, (ii) its acceleration 10mm from the centre, (iii) its kinetic energy at the centre. At what point is the potential energy a maximum?
3 In simple harmonic motion, a mass of 0.1kg has an amplitude of 10 mm. Calculate (i) the maximum velocity and (ii) the maximum force on the mass, if the period of the motion is p /2 s.
4 A vibrating mass of 0.06 kg has an amplitude of 0.08 m and a period of 4s. Find the velocity, acceleration and kinetic energy at the middle of the motion. What is the maximum value of the kinetic energy during the motion?
5 Draw sketches of the variations of (i) the kinetic energy, (ii) the potential energy, (iii) the total energy of a particle during one cycle of s.h.m. Account for the appearance of the graphs.
