Question

For the simple harmonic motion equation d=5sin((pi/4)t), what is the period?

Answer 1

Let WolframAudio help you:

http://www.wolframalpha.com

Enter:
d=5sin(pi/4t)

Solution:
http://www.wolframalpha.com/input/?i=d%3 …

Look at the plots.

The variable t (period) is:
t = pi/(4sin^(−1)(d/5))

Answer 2

w = pi /4 = 2 pi f

1 /4 = 2 f

f = 1/8 = angular frequency
= 1 / period

period = 8 unit

Answer 3

period is :after what time will the body return to same phase..after what consecutive time interval will the body be at d=5...it will be at d=5 at t=2 (check it) and t=10(check it too!!)...so diff between them is 8 sec and so is the period..
else use the aforesaid formulas..