Finding amplitude of oscillator

AI Thread Summary
The discussion focuses on calculating the amplitude of a mass-spring oscillator with a mass of 200g oscillating at a frequency of 2.0 Hz. The period is determined to be 1/2 s, and the angular frequency is calculated as 4π rad/s. The user encounters difficulty in finding the amplitude due to the unknown phase constant (psi) in the equations of motion. It is suggested to use conservation of energy principles, noting that the maximum potential energy occurs when the spring is at its maximum extension, which corresponds to the amplitude. The spring constant can be derived using the relationship between period and mass.
natasgan
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Homework Statement


a 200g mass attached to a horizontal spring oscillates at a frequency of 2.0 Hz. At t=0s, the mass is at x=5.0 cm and has v=-30 cm/s. Determine:
a) period
b)angular frequency
c) AMPLITUDE


Homework Equations


x(t)=Acos(wt+psi)
v(t)=-Awsin(wt+psi)
w=2*pi*f
T=1/f

The Attempt at a Solution


I have solved for the period=1/2 s
I have also solved for angular frequency=2*pi*2=4*pi
However, I am confused about solving for amplitude. I thought that I could plug in 0.05 m and 0s to the x(t) formula, but I do not know psi (phase constant) so I am stuck.
 
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When solving for the amplitude, try using conservation of energy.

--> All energy in the system is potential energy when the spring is extended the most. (When the spring is extended the most, the length extended is the amplitude)

The spring constant you can get from

T=2*pi*sqrt(m/k)
 

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