Simple Harmonic Motion (SHM) Practice

A set of vocabulary-style flashcards covering key concepts, formulas, and relationships of Simple Harmonic Motion (SHM) based on standard physics problems.

Simple Harmonic Motion (SHM)

A type of oscillation where the acceleration of an object is proportional to its displacement from an equilibrium position and is always directed towards that equilibrium position.

Relationship between acceleration and displacement

In SHM, the ratio of the acceleration of the particle to its displacement from the equilibrium position is proportional to $T^{-2}$.

Total Energy in SHM ($E$)

The energy of the system, which is proportional to the mass of the object and the square of the amplitude ($E \text{ is proportional to } A^2$).

Time Period of a Pendulum on the Moon

The time period increases on the Moon because the acceleration of free fall ($g$) is smaller than on Earth, according to the relation T = 2\text{\pi}\sqrt{\frac{l}{g}}.

Time Period of a Mass-Spring System on the Moon

The time period remains unchanged compared to Earth because it depends only on the mass ($m$) and the spring constant ($k$) (T = 2\text{\pi}\sqrt{\frac{m}{k}}), not on the gravitational field strength.

Resultant Force on a Pendulum Bob

The resultant force on the bob of an oscillating simple pendulum is never zero during any point of the oscillation.

Angular Frequency (\text{\omega}) Independence

In a mass-spring system executing SHM, the angular frequency of the oscillation is independent of the initial displacement (amplitude) of the spring.

Evidence for Matter Waves

The phenomenon of electron diffraction provides experimental evidence for the existence of matter waves.

Kinetic Energy at Equilibrium

The kinetic energy ($E_k$) of a particle in SHM is at its maximum value when the particle passes through the equilibrium position ($x = 0$).

Kinetic Energy at Maximum Displacement

The kinetic energy ($E_k$) of a particle in SHM is zero when the particle is at its maximum displacement (amplitude).

Phase Difference for a path difference of $\frac{\lambda}{4}$

If two waves meet at a point with a path difference of one quarter wavelength ($\frac{\lambda}{4}$), the phase difference between them is \frac{\text{\pi}}{2} rad.

Maximum Acceleration in SHM

The magnitude of the maximum acceleration of an object in SHM can be expressed as a_{max} = \frac{4\text{\pi}^2 x_0}{T^2}, where $x_0$ is the amplitude and $T$ is the period.

Displacement Equation (Starting at Maximum Displacement)

The expression for displacement ($x$) as a function of time ($t$) when the object starts at maximum displacement ($x_0$) is x = x_0 \text{\cos}(\frac{2\text{\pi}}{T}t).

Angular Frequency Relationship

Angular frequency is related to the time period by the formula \text{\omega} = \frac{2\text{\pi}}{T}; if the period doubles, the angular frequency becomes \frac{\text{\omega}}{2}.