SHM calculations

A body performs simple harmonic motion.

What is the phase difference between the variation of displacement with time and the variation of acceleration with time for the body?

• 0

• π/4 rad

• π/2 rad

• π rad

A body moves with simple harmonic motion of amplitude A and frequency b/2π

What is the magnitude of the acceleration when the body is at maximum displacement?

•  zero

•  4π²Ab²

• Ab²

• 4π²A/b²

Which one of the following gives the phase difference between the particle velocity and the particle displacement in simple harmonic motion?

• π/4 rad

• π/2 rad

• 3π/4 rad

• 2π rad

A body is in simple harmonic motion of amplitude 0.50 m and period 4π seconds. What is the speed of the body when the displacement of the body is 0.30 m?

• 0.10 m s^–1

• 0.15 m s^–1

• 0.20 m s^–1

• 0.40 m s^–1

A body moves in simple harmonic motion of amplitude 0.90 m and period 8.9 s. What is the speed of the body when its displacement is 0.70 m?

• 0.11 m s^–1

• 0.22 m s^–1

• 0.40 m s^–1

• 0.80 m s^–1

A particle, whose equilibrium position is at Q, is set into oscillation by being displaced to P, 50 mm from Q, and then released from rest.  Its subsequent motion is simple harmonic, but subject to damping. On the first swing, the particle comes to rest momentarily at R, 45 mm from Q. During this first swing, the greatest value of the acceleration of the particle is when it is at

• P

• Q

• R

• P and R

A mass M hangs in equilibrium on a spring. M is made to oscillate about the equilibrium position by pulling it down 10 cm and releasing it. The time for M to travel back to the equilibrium position for the first time is 0.50 s. Which line, A to D, is correct for these oscillations?

• amplitude = 10 cm, period = 1.0 s

• amplitude = 10 cm, period = 2.0 s

• amplitude = 20 cm, period = 2.0 s

• amplitude = 20 cm, period = 1.0 s

A body is in simple harmonic motion of amplitude 0.50 m and period 4π seconds. What is the speed of the body when the displacement of the body is 0.30 m?

• 0.10ms⁻¹

• 0.15ms⁻¹

• 0.20 m s⁻¹

• 0.40 m s⁻¹

The diagrams show the variation of velocity and acceleration with time for a body undergoing simple harmonic motion. Which one of the following is proportional to the change in momentum of the body during the time covered by the graphs?

• The area enclosed by the velocity-time graph and the time axis

• The gradient of the velocity-time graph at the point P

• The area enclosed by the acceleration-time graph and the time axis

• The gradient of the acceleration-time graph at the point Q

A particle is oscillating with simple harmonic motion described by the equation: s = 5 sin (20πt)

How long does it take the particle to travel from its position of maximum displacement to its mean position?

• 1/40 s

• 1/20 s

• 1/10 s

• 1/5 s