# Oscillations - Finding Displacement at a Speed, Given Displacement at Another Speed

## Homework Statement

A 0.10kg mass is on a spring with k = 0.10 N/m. At time t=0s it crosses x=0m with a velocity of 2.0m/s. What is its displacement when v=1.0m/s?

## Homework Equations

x(t) = Acos(wt + $$\varphi$$)
v(t) = -wAsin(wt + $$\varphi$$)
w = $$\sqrt{k/m}$$

## The Attempt at a Solution

According to the question...shouldn't v(0) = 2? When a plug those numbers into the v(t) equation I get: v(0) = -wAsin(0) = 0...in other words, v(0) = 0...what am I missing here? I have an idea of where to go from here, but if someone could clarify how I'm supposed to start, that would be great. Thanks for your time.

rock.freak667
Homework Helper

## The Attempt at a Solution

According to the question...shouldn't v(0) = 2? When a plug those numbers into the v(t) equation I get: v(0) = -wAsin(0) = 0...in other words, v(0) = 0...what am I missing here? I have an idea of where to go from here, but if someone could clarify how I'm supposed to start, that would be great. Thanks for your time.

Remember you have x=Acos(ωt+φ) so x(0) = Acosφ

v=Aωsin(ωt+φ), v(0) does not give you Aωsin(0), remember there is still φ which is unaffected by t being equal to zero.

Remember you have x=Acos(ωt+φ) so x(0) = Acosφ

v=Aωsin(ωt+φ), v(0) does not give you Aωsin(0), remember there is still φ which is unaffected by t being equal to zero.

Okay - not sure if this route even needs to be undertaken at all though...does this work?:

Etotal = $$\frac{1}{2}$$kx2 + $$\frac{1}{2}$$mv2

Etotal = 0 + $$\frac{1}{2}$$0.1(2)2

Etotal = 0.2

0.2 = $$\frac{1}{2}$$(0.1)x2 + $$\frac{1}{2}$$0.1(1)2

x = 1.7

Does that work?

rock.freak667
Homework Helper

Yes that works just as well.