Question

The function
x = (4.8 m) cos[(3πrad/s)t + π/6 rad]
gives the simple harmonic motion of a body. At t = 5.6 s, what are the (a) displacement, (b) velocity, (c) acceleration, and (d) phase of the motion? Also, what are the (e) frequency and (f) period of the motion?

Answer 1

compare the given equation with

x = A*cos(w*t + phi)

A = 4.8 m
w = 3*pi rad/s
phi = pi/6 rad

at t = 5.6 s
a)

x = 4.8*cos(3*pi*5.6 + pi/6)

= -4.77 m

b) v = dx/dt

= A*w*(-sin(w*t + phi))

at t = 5.6 s

v = -4.8*3*pi*sin(3*pi*5.6 + pi/6)

= -4.73 m/s

c) a = dv/dt

= -A*w^2*cos(w*t + phi)

= -A*w^2*x

= -4.8*(3*pi)^2*(-4.77)

= 2034 m/s^2

d) phase of the motion = w*t + phi

= 3*pi*5.6 + pi/6

= 53.3 rad

e) frequency, f = w/(2*pi)

= 3*pi/(2*pi)

= 1.50 Hz

f) T = 1/f

= 1/1.5

= 0.67 s