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