An object moves in simple harmonic motion described by the g

An object moves in simple harmonic motion described by the given? equation, where t is measured in seconds and d in inches. Find a. the maximum displacement b. the frequency c. the time required for one cycle.

Solution

d = - 8cos ( pi/4 ) t

standard equation of simple harmonic motion is

d = A cos wt

where, A = amplitude

w = angular frequency

frequency = w / 2pi

comparing the two equations we get

maximum displacement = 8

frequency = pi/4 / 2pi = 1/8

time required for 1 cycle = f = 1 /T = T = 1/f

therefore Time = 8 seconds