- #1

frozenguy

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## Homework Statement

Suppose a particle of mass 0.240 kg acted on by a spring undergoes simple harmonic

motion. We observe that the particle oscillates between x = 0.200 m and x = - 0.200 m

and that the period of the oscillation is 1.20 s. At time t = 0, the particle is at x = 0 and

has positive vx.

(a) Beginning with whatever general harmonic solution you prefer to use, derive

equations for x(t), vx(t), and ax(t). The only symbols your results may contain are ω and t.

Be sure to use SI units and include units in your results.

(b) Calculate the angular frequency of the oscillation and the spring constant of the

spring.

(c) At what time will the mass reach x = -0.100 m? Calculate vx at that time.

(d) Derive equations for K(t) and U(t). The only symbols your results may contain are ω

and t. Be sure to use SI units and include units in your results.

(e) What is the total energy of the motion?

## Homework Equations

a.) I was thinking I could use the (d^2y)/(dt) + (k/m)y=0

Thats the harmonic oscillator differential equation.

d.) The total energy is governed by how much the spring is initially compressed or stretched right? So Ui + Ki = Uf + Kf?

## The Attempt at a Solution

Can I derive the three equations by integrating the harmonic oscillator diff eq?

I think I'm sure I can get b. and c. once I can get these derived. When it asks to use any of the general solutions, is that referring to the equations using cosine and sine functions and phi?