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What is Simple Harmonic Motion (SHM)?
Motion where the restoring force is proportional to displacement and acts in the opposite direction.
What is the definition of oscillation?
The back-and-forth movement of an object around its equilibrium position.
Define amplitude (A).
The maximum displacement from the equilibrium position.
What is the period (T)?
Time for one complete cycle of motion. Measured in seconds.
Define frequency (f).
Number of cycles per second. Measured in Hertz (Hz).
What is restoring force?
Force that pulls an object back to its equilibrium. Always points towards equilibrium.
Define spring constant (k).
Measure of a spring's stiffness. Higher k means a stiffer spring.
What is angular frequency (ω)?
Rate of oscillation in radians per second. $ω = 2πf = \frac{2π}{T}$
Define phase angle (φ).
Initial angle of the oscillation at t=0. Determines the starting position.
What is resonance?
When an object vibrates with maximum amplitude because of an external force at its natural frequency.
What are the key differences between frequency (f) and angular frequency (ω)?
Frequency (f): Cycles per second (Hz). | Angular Frequency (ω): Rate of oscillation in radians per second (rad/s).
Compare and contrast potential and kinetic energy in a mass-spring system during SHM.
Potential Energy: Stored in the spring, maximum at max displacement. | Kinetic Energy: Energy of motion, maximum at equilibrium.
Compare and contrast potential and kinetic energy in a pendulum system during SHM.
Potential Energy: Gravitational potential energy, maximum at max height. | Kinetic Energy: Energy of motion, maximum at lowest point.
How to calculate the period of a mass-spring system?
1. Identify the mass (m) and spring constant (k). 2. Use the formula: $T = 2π\sqrt{\frac{m}{k}}$
How to calculate the period of a simple pendulum?
1. Identify the length of the pendulum (L) and the acceleration due to gravity (g). 2. Use the formula: $T = 2π\sqrt{\frac{L}{g}}$
How to find maximum potential energy in SHM for a spring?
1. Identify the spring constant (k) and amplitude (A). 2. Use the formula: $U_{max} = \frac{1}{2}kA^2$
How to find maximum kinetic energy in SHM?
1. Identify the mass (m) and maximum velocity (v_max). 2. Use the formula: $K_{max} = \frac{1}{2}mv_{max}^2$
How to determine total energy (E) in SHM?
1. Find either the maximum potential energy (U_max) or the maximum kinetic energy (K_max). 2. Total energy: $E = U_{max} = K_{max}$