Defining Simple Harmonic Motion (SHM) - AP Physics 1

Write the equation for displacement in SHM.

$x(t) = A\cos(\omega t + \phi)$ . This cosine function describes position as a function of time.
State the formula for acceleration in SHM.

$a(t) = -A\omega^2\cos(\omega t + \phi)$ . Acceleration is the time derivative of velocity in SHM.
State the equilibrium position in SHM.

The equilibrium position is where the net force is zero. At this point, the object experiences no acceleration.
How is the natural frequency of a mass-spring system defined?

$f_0 = \frac{1}{2\pi}\sqrt{\frac{k}{m}}$ . This is the frequency at which the system naturally oscillates.
What is the total mechanical energy in SHM?

$E = \frac{1}{2}kA^2$ . Total energy is conserved and proportional to amplitude squared.
What is the phase constant in SHM?

The phase constant determines the initial position and direction. It sets the starting conditions at time zero.
How does damping affect SHM?

It reduces the amplitude and can eventually stop the motion. Energy is gradually lost to friction and other dissipative forces.
Define amplitude in the context of SHM.

Amplitude is the maximum displacement from equilibrium. It represents the farthest distance the object travels from center.
Define the term 'frequency' in SHM.

Frequency is the number of oscillations per unit time. It measures how many complete cycles occur in one second.
State Hooke's Law.

Hooke's Law: $F = -kx$ . This is the fundamental equation describing elastic force behavior.
What happens to SHM's period if spring constant $k$ increases?

The period decreases. Stiffer springs cause faster oscillations with shorter periods.
What is the angular frequency formula in SHM?

$\omega = \sqrt{\frac{k}{m}}$ . This relates the system's physical properties to oscillation rate.
What is the unit of angular frequency $\omega$ ?

Radians per second (rad/s). This measures how fast the phase angle changes over time.
What determines the period of a simple pendulum?

The length of the pendulum and gravity. Mass of the pendulum does not affect the period.
What is the condition for SHM to occur?

The restoring force must be proportional to displacement. This linear relationship creates the characteristic sinusoidal motion pattern.
How does potential energy vary in SHM?

$U = \frac{1}{2}kx^2$ . Potential energy is maximum at maximum displacement positions.
State the relationship between frequency and period.

$f = \frac{1}{T}$ . They are mathematical reciprocals of each other.
What is the kinetic energy formula in SHM?

$K = \frac{1}{2}mv^2$ . Kinetic energy is maximum when passing through equilibrium position.
Define damping in the context of SHM.

Damping is the reduction of amplitude over time. Friction and air resistance cause energy loss over time.
What does the negative sign in $F = -kx$ signify?

The force is in the opposite direction of displacement. This ensures the force always acts toward equilibrium position.
Identify the energy forms present in SHM.

Kinetic energy and potential energy. Energy continuously transforms between these two forms during oscillation.
Identify the phase of an object at maximum displacement in SHM.

$\omega t + \phi = 0 \text{ or } \pi$ . At these phases, velocity is zero and displacement is maximum.
What is the frequency unit in SHM?

Hertz (Hz). Named after Heinrich Hertz, it represents cycles per second.
What role does gravity play in a simple pendulum's motion?

Gravity acts as the restoring force. The component of weight provides the restoring force for pendulums.
State the formula for the period of a mass-spring system in SHM.

$T = 2\pi \sqrt{\frac{m}{k}}$ . Period depends on mass and spring constant, independent of amplitude.
Describe the energy transformation in SHM.

Energy oscillates between kinetic and potential. Total mechanical energy remains constant throughout the motion.
How does mass affect the period of a mass-spring system?

The period increases with mass. Heavier masses oscillate more slowly due to greater inertia.
What is the effect of increasing the length $L$ of a pendulum on its period?

The period increases. Longer pendulums oscillate more slowly due to increased inertia.
What is the formula for velocity in SHM?

$v(t) = -A\omega\sin(\omega t + \phi)$ . Velocity is the time derivative of the displacement equation.
What is the effect of amplitude on SHM's period?

Amplitude does not affect the period. This is a unique property distinguishing SHM from other motions.
What is the significance of the term $A\omega$ in SHM velocity?

It represents the maximum speed. This occurs when the object passes through equilibrium position.
What is the formula for the period of a simple pendulum?

$T = 2\pi \sqrt{\frac{L}{g}}$ . Period depends only on length and gravitational acceleration.
What is resonance in SHM?

Resonance occurs when a system oscillates at its natural frequency. This can cause large amplitude oscillations and potential system damage.
What is Simple Harmonic Motion (SHM)?

SHM is periodic motion where the restoring force is proportional to displacement. This defines the characteristic linear relationship between force and displacement.
Describe the motion when SHM is undamped.

Oscillations continue indefinitely with constant amplitude. No energy is lost, so motion continues perpetually.
Describe the motion of an object in SHM.

The object moves back and forth about an equilibrium position. This repetitive motion is the defining characteristic of SHM.
State the relationship between period and angular frequency.

$T = \frac{2\pi}{\omega}$ . These quantities are inversely proportional to each other.
What is the significance of the phase constant $\phi$ in SHM?

Determines the initial angle at $t=0$ . It shifts the entire motion pattern in time.
Identify the restoring force in a mass-spring system.

$F = -kx$ . Hooke's Law shows force proportional to displacement with spring constant.

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