Simple Harmonic Motion and Oscillations Practice

Flashcards covering periodic and oscillatory motion, Simple Harmonic Motion (SHM) properties, energy conservation, and experimental pendulum calculations based on the lecture transcript.

Periodic Motion

A motion that repeats itself at regular intervals of time, such as Saturn moving with uniform angular speed along its orbit or a bird circling a clock tower.

Oscillatory Motion

A specific type of periodic motion where an object moves back and forth about a fixed mean position, such as a bird flapping its wings or a vibrating tuning fork.

Time Period ($T$) of a Pendulum in Space

The duration of one oscillation which becomes infinite in space because the value of acceleration due to gravity ($g$) used in the formula T = 2\text{\pi} \sqrt{\frac{L}{g}} is zero.

AC Power Zero Points

In a 50 Hz power supply where voltage varies as a sine function, the power becomes zero $100$ times per second, as it completes $50$ oscillations and reaches zero twice per cycle.

SHM Acceleration-Displacement Relationship

The mathematical relationship where acceleration ($\beta$) is directly proportional to the negative displacement ($y$), such as $\beta = -5y$.

Center of Gravity Effect on Pendulum Period

As water flows out of a hollow sphere, the center of gravity first lowers, increasing the effective length ($L$) and time period, and then returns to the center when empty, decreasing the period.

Heartbeat Frequency Calculation

The conversion of a time period of $0.8\,s$ into beats per minute, calculated as $\frac{60}{0.8} = 75\,\text{beats/min}$.

Necessary Relation for S.H.M.

The requirement that the restoring force (or acceleration) must be directly proportional to the displacement from the equilibrium position.

Resonance in Buildings

A scientific phenomenon where the magnitude of frequency of earthquake aftershocks is close to the natural frequency of buildings, leading to collapse.

Graph Slope ($L$ vs $T^2$)

The slope $S$ of a graph plotting length against the square of the time period; when multiplied by 4\text{\pi}^2, it represents the value of acceleration due to gravity ($g$).

Energy at Displacement $A/\sqrt{2}$

The specific point in SHM where the kinetic energy of the particle is exactly equal to its potential energy.

Angular Frequency ($\omega$)

The rate of change of angular position, related to the time period by the formula \omega = \frac{2\text{\pi}}{T}.

Force Constant of a Simple Pendulum

A property that is directly proportional to the mass of the bob, derived from the restoring force relation $F = -\left(\frac{mg}{L}\right)y$.

Combined Displacement Amplitude

The resultant amplitude of a particle moving according to $y = 3 \sin(314t) + 4 \cos(314t)$, which is determined to be $5\,\text{meters}$.

Stiff vs. Delicate Spring Oscillation

Between two springs, the stiffer one will have a greater frequency of oscillation for a given load compared to the delicate one.

Pendulum Watch in Artificial Satellites

A device that cannot be used in a satellite because in a weightless environment ($g = 0$), the time period becomes infinite and the pendulum will not oscillate.

Uniform Circular Motion Projection

The one-dimensional projection of a body moving in uniform circular motion onto its diameter, which is proven to be Simple Harmonic Motion.