# Harmonic Motion

johan146

## Homework Statement

A spring holds a weight of 800 g. The spring is set in a harmonious swing. The frequency f for the oscillation is 1.4 Hz. When the weight is 5 cm above the equilibrium position on the way upwards, a velocity of 1.1 m / s is noted
a) Determine the amplitude of the movement.
b) What is the acceleration when the weight is 2 cm above the equilibrium?

## Homework Equations

Y=A⋅sinωt
f = 1/T
MV^2/2 + kY^2/2=kA^2/2

## The Attempt at a Solution

I first attempted to calculate the amplitude of the movement by using the first equation but since i didn't have the time of the spring i crossed over that calculation, i latet tried using the 2 later equations together but i never managed to get a resonable result from my calculation

The English in the question might be a bit wrong, not my mother tongue so i had to translate the question from Swedish so bare with me :)
Any help is appreciated! Thanks in advance

Last edited by a moderator:

frequency f for the oscillation is 1.4 Hz .... f = 1/T

but since i didn't have the time of the swing
What does this say about the period (time of the swing)?

By now you may have solved your problem but if not...
consider 0.5 = Asin(wt) and 1.1 = wAcos(wt)

johan146
By now you may have solved your problem but if not...
consider 0.5 = Asin(wt) and 1.1 = wAcos(wt)
Does t in these equations equal the period T?

Does t in these equations equal the period T?
No, ##t## is the time elapsed. ##w## is the angular frequency, which does relate to the period by ##w=2\pi/T##.

johan146
No, ##t## is the time elapsed. ##w## is the angular frequency, which does relate to the period by ##w=2\pi/T##.
Oh okey, but how to you find out what t is in this case? I assume that the velocity is not constant so we can't use S = Vt

Check my post above. Two equations, two unknowns. Enter what you know and solve.

• johan146