How to find magnitude of initial displacement?

1. Mar 7, 2013

Sneakatone

A mass of 130 g is held by a horizontal spring constant 22 N/m. It is displaced from its equilibrium position and released from the rest. As it passes through its equilibrium position, its speed is 4.2 m/s.

a) find work done on the spring.
w=1/2mv^2
1/2(.13kg)(4.2)^2= 1.14 (correct)

b) what is the magnitude of the initial displacement?
I dont know what to do for this , Im guessing were suppose to find distance but I dont know how.

2. Mar 7, 2013

You have the work correct. Now you have to know how much displacement has been done for that amount of work.

The equation for the force of a spring is F = -kx, where x is the distance displaced from equilibrium. Thus, the work, which is ∫F dx = -k x^2 / 2. The negative sign signifies that the work is done on the system.

Thus, your value for work, W = k x^2 / 2, so x = √(2W/k).

3. Mar 7, 2013

Sneakatone

can I do 0.13kg/22=0.005 m to get displacement?

4. Mar 7, 2013

Sneakatone

never mind x=sqrt(2*1.14/22)=0.32 m
Thank you!

5. Mar 7, 2013