For an object at Simple Harmonic Motion (SMH), we can
write the equation of motion as:
x(t) = A cos[(2 pi/P) t]
where
P is the period = 0.9
t is time
A is the amplitude = 0.32
Therefore for this object we have the equation:
x(t) = 0.32 cos[(2 pi/0.9) t]
A. Calculate t from
x = 0.320 m to x = 0.160 m
We know that at t = 0 the value of x would be: x=0.32 since cos 0 = 1. So we only have to find the value of t when x =0.16m. Using the equation:
0.16 = 0.32 cos[(2 pi/0.9) t]
0.5 = cos[(2pi/0.9) t]
pi/3 = (2 pi/0.9)t
t = 0.15 s
Therefore it takes 0.15 s to go from 0.32 to 0.16m
B. Calculate t from x = 0.160 m to x = 0
The time at which x = 0 is:
0 = 0.32 cos[2 pi/0.90)t]
pi/2 = (2 pi/0.90)t
t = 0.225s
Therefore it takes 0.225s-0.150s = 0.075s to go from 0.16 to 0 m.
