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## Homework Statement

A mass m sits on a horizontal frictionless surface and is attached to a wall by means of a spring having force constant k. The mass is now subjected to an additional force of the form.

F(t) = Acosbt

(a) Write the equation of motion for this mass.(b) What is the solution to this equation which satisfies the conditions x(t==0) = 0; and v(t=0) = 0?(c) Assume now that the driving frequency is twice the natural frequency of the oscillator. What is

the period of the motion?(d) Write an expression for the power delivered to the mass by the external force.(e) Integrate your expression for the power over one cycle of the motion. Is this the result youwould expect? Explain.

## Homework Equations

So mx''= -kx + Acos(bt)

ω

_{0}

## The Attempt at a Solution

Solving for the initial conditions I found that

x = [A/m(ω

^{2}-ω

_{0}

^{2})](cos(bt) - cos(ωt))

Is this the correct form to find the period of motion?