Defining Simple Harmonic Motion (SHM) - AP Physics C Mechanics

1. Define damping in the context of SHM.

   Reduction of amplitude over time due to resistive forces. Friction and air resistance cause energy loss over time.

2. What is the total mechanical energy in SHM?

   $E = \frac{1}{2} k A^2$. Energy is proportional to amplitude squared.

3. Identify the expression for the period of a simple pendulum.

   $T = 2\pi\sqrt{\frac{L}{g}}$. Valid only for small angular displacements (less than 15°).

4. What is the relationship between frequency and period in SHM?

   $f = \frac{1}{T}$. Frequency is the reciprocal of period.

5. What is the phase angle in SHM?

   Determines initial state of motion. Sets the timing and starting conditions of oscillation.

6. In undamped SHM, what remains constant?

   Total mechanical energy. No energy is lost to friction or other dissipative forces.

7. In SHM, what is the potential energy at maximum displacement?

   $U = \frac{1}{2} k A^2$. All energy is potential when kinetic energy is zero.

8. In SHM, what is the phase difference between velocity and acceleration?

   $\frac{\pi}{2}$ or 90 degrees. Velocity leads position by 90°, acceleration leads velocity by 90°.

9. In SHM, what is the maximum velocity?

   $v_{max} = A\omega$. Occurs when the object passes through equilibrium position.

10. Express the position as a function of time in SHM.

    $x(t) = A \cos(\omega t + \phi)$. Cosine function represents position starting from maximum displacement.

11. What is the unit of angular frequency?

    Radians per second (rad/s). Measures rate of phase change in oscillatory motion.

12. What is the condition for SHM in terms of displacement and force?

    Force proportional and opposite to displacement. Restoring force always points toward equilibrium position.

13. In SHM, when is kinetic energy maximum?

    At the equilibrium position. All potential energy converts to kinetic at equilibrium.

14. What is resonance in the context of SHM?

    Large amplitude oscillations when frequency matches natural frequency. Driving frequency equals natural frequency for maximum energy transfer.

15. How does mass affect the period of a mass-spring system in SHM?

    Period increases with mass. Heavier objects oscillate more slowly due to greater inertia.

16. What defines Simple Harmonic Motion (SHM)?

    Motion where restoring force is proportional to displacement. This creates oscillatory motion with constant period and frequency.

17. What is the term for the equilibrium position in SHM?

    Position where the net force is zero. Reference point where restoring force equals zero.

18. How does spring constant affect the period of a mass-spring system in SHM?

    Period decreases with increasing spring constant. Stiffer springs produce faster oscillations.

19. What is the relationship between angular frequency and frequency?

    $\omega = 2\pi f$. Angular frequency is frequency multiplied by $2\pi$.

20. State Hooke's Law for springs.

    $F = -kx$. Linear relationship between force and displacement for elastic materials.

21. State the expression for the period of a mass-spring system.

    $T = 2\pi\sqrt{\frac{m}{k}}$. Period is independent of amplitude in SHM.

22. In SHM, what is the maximum acceleration?

    $a_{max} = A\omega^2$. Occurs at maximum displacement from equilibrium.

23. State the condition for small angle approximation in pendulum SHM.

    Angle $\theta$ must be less than 15 degrees. Ensures $\sin(\theta) \approx \theta$ for linear restoring force.

24. Define the term 'amplitude' in SHM.

    Maximum displacement from the equilibrium position. Represents the maximum energy state of the oscillating system.

25. How is energy conserved in SHM?

    Energy transitions between kinetic and potential forms. Kinetic and potential energy oscillate while total remains constant.

26. What is the velocity as a function of time in SHM?

    $v(t) = -A\omega \sin(\omega t + \phi)$. Velocity is the time derivative of position.

27. What remains constant in a simple pendulum undergoing SHM?

    The length of the pendulum. Length determines the period of oscillation.

28. What effect does increasing length have on a pendulum's period?

    Period increases. Longer pendulums take more time to complete one cycle.

29. What is the phase relationship between displacement and acceleration in SHM?

    They are in phase opposition. They differ by 180° or $\pi$ radians.

30. What is the equation for angular frequency in SHM?

    $\omega = \sqrt{\frac{k}{m}}$. Derived from $F = ma$ and $F = -kx$ for mass-spring systems.

31. What is the effect of gravity on the period of a simple pendulum?

    Period decreases with increased gravity. Stronger gravity increases restoring force and frequency.

32. In a mass-spring system, what is the natural frequency?

    $\frac{1}{2\pi}\sqrt{\frac{k}{m}}$. Frequency when system oscillates freely without external forces.

33. When does a simple pendulum exhibit SHM?

    For small angular displacements. Small angle approximation makes restoring force proportional to displacement.

34. State the formula for the restoring force in SHM.

    $F = -kx$. Hooke's law where $k$ is spring constant and $x$ is displacement.

35. Define 'natural frequency' in SHM.

    Frequency at which a system oscillates when not disturbed. Characteristic frequency determined by system properties only.

36. What is the acceleration as a function of time in SHM?

    $a(t) = -A\omega^2 \cos(\omega t + \phi)$. Acceleration is the second time derivative of position.

37. What is the restoring force for a simple pendulum in SHM?

    $F = -mg\sin(\theta)$. Gravitational component tangential to the arc provides restoring force.

38. What is the phase constant in SHM?

    Initial angle in the argument of the cosine or sine function. Determines starting position and velocity of the oscillation.

39. Identify the dimensionless unit for phase.

    Radians. Phase has no physical dimensions.

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