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Physics Help Please! *********Challenge of the day***********?
A 200g ball attached to a spring with spring constant
2.70N/m oscillates horizontally on a frictionless table. Its velocity is 22.0cm/s when x= -5.00cm.
A) What is the amplitude of oscillation? A= ???cm
B) What is the speed of the ball when x= 3.00cm? v= ???cm/s
Loosing my last nerve on this problem, please help!!!!
We need to assume that the equilibrium position is x=0
Then x(t) = A sin (omega t)
x'(t) = A omega cos (omega t)
The frequency of a mass on a spring is:
omega = sqrt (k/m)
sin(omega t) = x(t) / A
cos (omega t) = sqrt (1 - sin(omega t) ^2)
= sqrt (1 - (x(t) / A)^2 )
= x'(t) / A omega
A^2 - x(t)^2 = x'(t)^2 / omega^2
A = sqrt (m x'(t)^2 / k + x(t)^2)
They give you the mass, spring constant, velocity, and position. Plugnchug.
To get B), solve the equation above for x'(t) in terms of A (which is now known) and x(t).
x'(t) = omega^2 (A^2 - x(t)^2)
= k (A^2 - x(t)^2) / m
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