Question

The maximum speed of a mass attached to a spring is vmax = 0.438 m/s, while the maximum acceleration is 1.53 m/s2. What is the maximum displacement of the mass? (Answer: 0.125m)

Answer is provided above. Please show all work on how to get the answer. Thank you.

Answer 1

x = A sin w t
v = A w cos wt
a = -w^2 A sin wt = -w^2 x
so
A w = .438 or w = .438/A
A w^2 = 1.53
so
A *(.438)^2/A^2 = 1.53
so
1.53 A = .192
A = .125 m

Answer 2

max speed=max PE
1/2 m v^2= 1/2 kx^2

but me know max force=kx
and force= ma so
kx=1.53m

1/2 mv^2=1/2 1.53m*x
solve for x, m divides out.

x=v^2/1.53 check that.