Simple Harmonic Motion Quiz

Study Notes

Simple Harmonic Motion (SHM) is a type of oscillatory motion, where the restoring force is proportional to the negative of the displacement.
Displacement is measured from the equilibrium point, which is the point where the spring is neither stretched nor compressed.
The force exerted by the spring is given by Hooke’s Law: F = -kx, where k is the spring constant.
Amplitude is the maximum displacement.
Period is the time required to complete one cycle.
Frequency is the number of cycles completed per second.

The potential energy of a spring is given by: PE = 1/2 kx^2
The total mechanical energy of the system is conserved in a frictionless system: E = KE + PE.
When the mass is at the limits of its motion, the energy is all potential.
When the mass is at the equilibrium point, the energy is all kinetic.
The maximum velocity of the mass can be calculated using the equation: v = sqrt(k/m) * A
The velocity of the mass as a function of position can be calculated using the equation: v = sqrt(k/m) * sqrt(A^2 - x^2)

The period of SHM is the time it takes for one complete cycle of motion.
The frequency of SHM is the number of cycles per second.
The displacement of an object in SHM can be described using a sinusoidal function (sine or cosine).
The period, frequency, and amplitude of SHM are related by the following equations:
- T = 2π√(m/k)
- f = 1/T = (1/2π)√(k/m)
The time period in SHM is determined by the mass and the spring constant.

A simple pendulum consists of a mass at the end of a lightweight cord.
The period of oscillation of a simple pendulum depends on the length of the pendulum and the acceleration due to gravity (g)
For Small oscillations (less than 10°), the period of a simple pendulum formula is: T = 2π√(L/g)
The period of a simple pendulum is independent of the mass of the bob.

Damped harmonic motion is harmonic motion with a frictional or drag force. It occurs when a system experiences energy loss due to friction or other dissipative forces.
If the damping is small, the oscillations gradually decrease in amplitude over time.
Critical damping is the optimal damping scenario where it returns to equilibrium quickly without oscillation.
Overdamping occurs when the damping is significant, which slows the system down and takes a long time to reach equilibrium.

Forced vibrations occur when there is a periodic driving force. This force may or may not have the same period as the natural frequency of the system.
Resonance occurs when the frequency of the driving force is equal to the natural frequency of the system.
At Resonance, the amplitude of the oscillations becomes very large.

Wave motion is the transfer of energy through a medium or space without the transfer of matter.
A wave is a disturbance that propagates through a medium or space, transferring energy.

There are types of waves: Transverse waves and Longitudinal waves.
In a transverse wave, the direction of wave propagation is perpendicular to the direction of particle motion.
In a longitudinal wave, the direction of wave propagation is parallel to the direction of particle motion.

Waves carry energy. The energy carried by a wave is related to its amplitude and frequency.
The intensity of a wave is the power per unit area and is proportional to the square of the amplitude.

Reflection occurs when a wave encounters a boundary and changes direction.
Transmission occurs when a wave passes through a boundary, continuing in a different medium.

The principle of superposition states that when two or more waves meet at a point, the displacement at that point is the sum of the displacements of the individual waves.
In constructive interference, the amplitudes of the waves add up, resulting in a larger amplitude.
In destructive interference, the amplitudes of the waves subtract from each other, resulting in a smaller amplitude.

A standing wave is formed when two waves of equal amplitude and frequency traveling in opposite directions interfere.
Nodes are points of zero displacement, and antinodes are points of maximum displacement.
Resonance occurs when a standing wave is formed in a system, amplifying the oscillations.

Refraction is the change in direction of a wave as it passes from one medium to another.
Refraction occurs because the speed of the wave changes as it enters a new medium.

Diffraction is the spreading out of a wave as it passes through an opening or around an obstacle.
The amount of diffraction depends on the wavelength of the wave and the size of the opening or obstacle.

A traveling wave can be represented mathematically using a sinusoidal function.
The wave equation is: y(x,t) = A sin(kx - ωt + φ). Where y is the displacement, A is the amplitude, k is the wave number, x is the position, ω is the angular frequency, t is the time, and φ is the phase constant.