# Homework Help: Simple Harmonic Motion and speed of mass

1. Nov 30, 2014

### e^(i Pi)+1=0

1. The problem statement, all variables and given/known data

A mass-spring system is oscillating with an amplitude of 10.0 cm. What is the speed of the mass at a location where the kinetic energy of the mass and the potential energy of the spring are equal?

I want to know if it's possible to solve for just a number, that is, not in terms of k and m. Also if my answer is right as it is. Thanks.

2. Relevant equations

3. The attempt at a solution

Force equals ma and also -kx
ma = -kx
ma+kx = 0
x''+(k/m)x = 0

Solve the differential equation, set x(0) = 0 and set the amplitude to 0.1 (in meters) to yield

x(t) = 0.1sin(√[k/m]t)

Differentiate to find v(t) and sub them into the equation

(1/2)mv2 = (1/2)kx2

I find t = π/4 and v(π/4) = -0.05√(2k/m)

2. Nov 30, 2014

### haruspex

No. Dimensional analysis: you are given a length, and you want a speed; you need a velocity or an acceleration etc. to connect those two dimensions.