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A 0.82-kg air cart is attached to a spring and allowed to oscillate.

Part A
If the displacement of the air cart from equilibrium is x=(10.0cm)cos[(2.00s?1)t+?], find the maximum kinetic energy of the cart.
Express your answer using two significant figures.

Part B
Find the maximum force exerted on it by the spring.
Express your answer using two significant figures.
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Added Mon, 06 Jul '15
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x = xmax*cos(omega*t + phi)

xmax is the amplitude
omega is the angular frequency
phi is the phase angle

For the mass-spring system, the theoretical omega is calculated as:
omega = sqrt(k/m)

We know omega and m, solve for k:
k = m*omega^2

And, since we know xmax and an expression for k, we can find the maximum strain potential energy, which is also equal, by energy conservation, to the maximum kinetic energy:
KEmax = SPEmax = 1/2*k*xmax^2

Thus:
KEmax = 1/2*m*omega^2*xmax^2

And, to find the maximum force exerted by the spring, just simply use Hooke's law. Forget about the negative sign, it isn't of interest to us. Yes, we do know it points opposite the displacement.
Fmax = k*xmax
Fmax = m*omega^2*xmax

Summary:
A) KEmax = 1/2*m*omega^2*xmax^2
B) Fmax = m*omega^2*xmax

A) KEmax = 0.5*0.82*4*0.1^2

= 0.0164J

b)Fmax = 0.82*4*0.1

= 0.328N
Edit
Added Mon, 06 Jul '15
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