Homework help: Harmonic Motion of a Spring and Block System

[KrhUhart]

Homework Statement

Part 1:

A 0.1 kg block attached to a spring of force constant 17.2 N/m oscillates with an amplitude of 16 cm. Find the the maximum speed of the block.

I solved this part using the equations for angular frequency and max velocity.

Part 2:

Find speed of the block when it is 8 cm from the equilibrium position. Answer in m/s.

Part 3:

Find acceleration in the same situation ^

Part 4:

Find the time it takes the block to move from amplitude 0cm, to amplitude 8 cm.

Homework Equations

ω = $\sqrt{}k/m$

Vm = Aω

V(t) = -AωSin(ωt)

a(t) = - Aω^2Cos(ωt)

The Attempt at a Solution

Part 1 i figured out:

ω = $\sqrt{}17.2/0.1$ = 13.1149 rads

Vm = (.16)(13.1149) = 2.09838 m/s


For part 2 i tried using the equation for velocity as a function of time. But I'm not sure how to solve the equation without the value for time. So far i have:

V(t) = -(0.08)(13.1149)Sin(13.1149(t))


Thank you everybody

 

[Hootenanny]

For part two, the displacement is half the amplitude so you are looking for a time $t$ such that $\cos(\omega t) = 1/2$.