AP Physics C: Mechanics Questions on Amplitude of SHM

📚 Quick Study Guide

• 📏 Amplitude (A): Maximum displacement from the equilibrium position.
• 🔄 SHM Condition: Restoring force is proportional to displacement: $F = -kx$.
• ⏱️ Period (T): Time for one complete oscillation. $T = 2\pi \sqrt{\frac{m}{k}}$ (mass-spring) or $T = 2\pi \sqrt{\frac{L}{g}}$ (simple pendulum).
• frequency (f): Number of oscillations per unit time. $f = \frac{1}{T}$
• ⚡ Total Energy (E): $E = \frac{1}{2}kA^2$, where $k$ is the spring constant and $A$ is the amplitude.
• 🚗 Velocity (v): Maximum velocity is at the equilibrium position: $v_{max} = A\omega$, where $\omega$ is the angular frequency.

🧪 Practice Quiz

1. A mass-spring system oscillates with an amplitude of 5 cm. If the total energy of the system is doubled, what is the new amplitude?
   1. 2.5 cm
   2. 5$\sqrt{2}$ cm
   3. 10 cm
   4. 20 cm
2. A simple pendulum has a length L and oscillates with an amplitude $\theta$. If the length is quadrupled, what happens to the period of the pendulum?
   1. The period is halved.
   2. The period remains the same.
   3. The period is doubled.
   4. The period is quadrupled.
3. A mass on a spring oscillates with simple harmonic motion. If the mass is increased by a factor of 9, what happens to the period?
   1. The period is divided by 3.
   2. The period remains the same.
   3. The period is multiplied by 3.
   4. The period is multiplied by 9.
4. If the amplitude of a simple harmonic oscillator is doubled, what happens to the maximum velocity?
   1. It remains the same.
   2. It is halved.
   3. It is doubled.
   4. It is quadrupled.
5. A spring with spring constant $k$ is stretched a distance $x$ from its equilibrium position. If the amplitude of the oscillation is doubled, what happens to the potential energy?
   1. It is halved.
   2. It remains the same.
   3. It is doubled.
   4. It is quadrupled.
6. A block oscillates on a horizontal frictionless surface attached to a spring. When the block is at its maximum displacement from equilibrium, its:
   1. Velocity is maximum and acceleration is zero.
   2. Velocity is zero and acceleration is maximum.
   3. Velocity and acceleration are both maximum.
   4. Velocity and acceleration are both zero.
7. The period of a mass-spring system is $T$. If both the mass and the spring constant are doubled, the new period will be:
   1. $T$
   2. $2T$
   3. $T/2$
   4. $T\sqrt{2}$