Question

A body vibrates in simple harmonic motion with an amplitude of 5 cm and a frequency of 0.50 Hz.

a) Calculate:
i) the maximum acceleration
ii) the maximum velocity
iii) the magnitude of the acceleration and velocity when the body is displaced 10 mm from its equilibrium position.

b) State the values of the constants A (in m) and W (in rad*s^-1) in the equation y = AsinWt which describes the motion of the body.

Answer 1

x = .05 sin [2 pi (.5)t]
= .05 sin 3.14159 t

v = .05 pi cos pi t
a = -.05 pi^2 sin pi t

max a = .05 pi^2
max v = .05 pi

10 mm = 1 cm = .01 m

x = .01 = .05 sin 3.14 t
sin 3.14 t = .20
3.14 t = 11.5 degrees = .201 radians
t = .0641 seconds

v = .05 pi cos 11.5 degrees
a = -.05 pi^2 sin 11.5 degrees