AP Physics C: Mechanics Unit 6: Oscillations

In simple harmonic motion, a particle's position is $x(t)=0.3\cos (5t)$ m. What is the maximum acceleration?

A 0.4 kg mass on a spring ($k=160$ N/m) oscillates at $x=0.05$ m amplitude. What is the speed at $x=0.03$ m?

A mass $m=0.5$ kg on a spring ($k=200$ N/m) oscillates with amplitude $A=0.1$ m. What is the maximum speed?

A torsional pendulum has restoring torque $\tau =-\kappa \theta$ where $\kappa$ is the torsion constant and $I$ is the moment of inertia. What is the period of oscillation?

A mass $m$ is attached to two identical springs (each constant $k$) in parallel (both springs pull on the mass simultaneously). What is the effective spring constant and resulting oscillation frequency?

A 0.4 kg mass on a spring ($k=160$ N/m) is released from rest at $x=0.05$ m from equilibrium. Find the total mechanical energy.

A spring–mass system ($k=50$ N/m, $m=0.5$ kg) starts at rest at $x=0.2$ m from equilibrium. Find the time at which the speed first equals half its maximum value. ($\omega =10$ rad/s)

Show using calculus that $x(t)=A\cos (\omega t+\varphi )$ satisfies the SHM equation $\frac{d^{2}x}{d{t}^2}=-{\omega }^{2}x$. What does this verify?

A damped oscillator has equation $m\ddot{x}+b\dot{x}+kx=0$ with $b^2<4mk$. Which statement correctly describes the motion?

A mass–spring system has spring constant $k=400$ N/m and mass $m=1$ kg. What is the angular frequency of oscillation?

A spring–mass system ($k$, $m$) undergoes SHM. At $t=0$, $x_0=0.06$ m and $v_0=0.8$ m/s. Given $\omega =10$ rad/s, find the amplitude.

A simple pendulum of length $L=1$ m oscillates with small amplitude. What is its period? ($g=10$ m/s²)