# Driven damped oscillator

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1. Oct 16, 2015

### DoctorBozon

1. The problem statement, all variables and given/known data
A small block (mass 0.25 kg) attached to a spring (force constant 16 N/m) moves in one dimension on a horizontal surface. The oscillator is subject to both viscous damping and a sinusoidal drive. By varying the period of the driving force (while keeping the drive amplitude fixed), it is found that the mass oscillates with its largest steady state amplitude (0.30 m) when the driving force has a period of 1.00 second.

Find the maximum speed of the mass in this largest-amplitude steady state. Express your answer in meters per second

2. Relevant equations

D = A/√((ω022)2 + 4ω2β2)
ω02 = k/m
ωr2 = √(ω02-2β2)

3. The attempt at a solution

I know that the resonance frequency ωr = 2∏/1.00s
From this I can find my damping parameter
I know that D=0.30m

Since dX/dt = -Dωsin(ωt-δ) , where ω=ω0 for kinetic energy resonance.
Is my maximum speed of the mass in the largest-amplitude steady state just D*ω0

2. Oct 21, 2015