Displacement in SHM Quiz with Answers: AP Physics 1

📚 Quick Study Guide

• 📏 Displacement (x): The distance of the object from its equilibrium position.
• ⏱️ Period (T): The time taken for one complete oscillation.
• frequency (f): The number of oscillations per unit time; $f = \frac{1}{T}$.
• 🧮 Angular Frequency ($\omega$): $\omega = 2\pi f = \frac{2\pi}{T}$.
• 📝 Displacement Equation: $x(t) = A \cos(\omega t + \phi)$, where A is the amplitude and $\phi$ is the phase constant.
• 💡 Velocity Equation: $v(t) = -A\omega \sin(\omega t + \phi)$.
• ⚡ Acceleration Equation: $a(t) = -A\omega^2 \cos(\omega t + \phi) = -\omega^2 x(t)$.
• spring constant (k): $k = m\omega^2$, where m is mass.
• ⚖️ Total Energy (E): $E = \frac{1}{2}kA^2 = \frac{1}{2}m\omega^2A^2$.

🧪 Practice Quiz

1. A mass-spring system oscillates with an amplitude A. What is the displacement when the potential energy equals the kinetic energy?
   1. 0
   2. A/2
   3. A$\sqrt{2}$/2
   4. A
2. The displacement of an object in SHM is given by $x(t) = 5 \cos(2\pi t)$. What is the frequency of oscillation?
   1. 1 Hz
   2. 2 Hz
   3. $\pi$ Hz
   4. 2$\pi$ Hz
3. An object in SHM has a period of 4 seconds. What is its angular frequency?
   1. $\pi$/2 rad/s
   2. $\pi$ rad/s
   3. 2$\pi$ rad/s
   4. 4$\pi$ rad/s
4. A mass attached to a spring oscillates with SHM. If the amplitude is doubled, what happens to the total energy?
   1. It remains the same.
   2. It doubles.
   3. It quadruples.
   4. It halves.
5. The displacement of a particle in SHM is given by $x(t) = 2\cos(\frac{\pi}{2}t)$. What is the velocity at t = 1 second?
   1. 0
   2. $\pi$
   3. -${\pi}$
   4. 2
6. A simple pendulum has a length L and oscillates with a period T. If the length is increased to 4L, what is the new period?
   1. T/2
   2. T
   3. 2T
   4. 4T
7. What is the acceleration of an object in SHM when it is at its maximum displacement?
   1. 0
   2. Maximum
   3. Minimum
   4. Constant