What is Simple Harmonic Motion (SHM)?
SHM is periodic motion in which acceleration and restoring force are directed toward the equilibrium point and are proportional to displacement.
What is amplitude in SHM?
Maximum displacement from the equilibrium position, denoted as \( A \) (meters).
Define period \( T \) in SHM.
Time taken to complete one full oscillation.
Define frequency \( f \) in SHM.
Number of oscillations per second, measured in Hertz (Hz).
What is displacement in SHM?
\( x = r \sin(\omega t) \)
What is angular velocity in SHM?
\( \omega = \frac{\theta}{t} \)
Relation between linear and angular velocity?
\( v = \omega r \)
Expression for SHM velocity?
\( v = \omega r \cos(\omega t) = \pm \omega \sqrt{r^2 - x^2} \)
Maximum velocity in SHM?
\( v_{\text{max}} = \omega r \)
Expression for SHM acceleration?
\( a = -\omega^2 r \sin(\omega t) \)
What is maximum acceleration in SHM?
\( a_{\text{max}} = \omega^2 r \)
Period of a spring-mass system?
\( T = 2\pi \sqrt{\frac{m}{k}} \)
Period of a simple pendulum?
\( T = 2\pi \sqrt{\frac{l}{g}} \)
Period of a loaded test tube in liquid?
\( T = 2\pi \sqrt{\frac{m}{\rho g A}} \)
Period squared for spring system?
\( T^2 = \frac{4\pi^2 m}{k} \)
Period in terms of extension?
\( T = 2\pi \sqrt{\frac{e}{g}} \)
What is free vibration?
Vibration where energy remains constant and amplitude stays unchanged.
What is damped vibration?
Vibration where energy is lost over time, reducing amplitude and frequency.
What is forced vibration?
Vibration maintained by an external periodic force.
Give an example of forced vibration.
Vibration of a table surface when a tuning fork is pressed on it.
What is resonance?
A condition where a vibrating object forces another to vibrate at its natural frequency.
When does resonance occur?
When the frequency of external force equals the natural frequency of the system.
What happens at resonance?
Maximum amplitude and energy transfer occur.
Example of mechanical resonance?
Collapse of a bridge when matched with natural frequency.
What is natural frequency?
Frequency at which an object naturally vibrates when undisturbed.
Expression for total energy in SHM using spring constant?
\( W = \frac{1}{2} k A^2 \)
Expression for total energy in SHM using mass and angular velocity?
\( W = \frac{1}{2} m \omega^2 A^2 \)
What is the source of restoring force in a spring system?
Hooke’s law: \( F = k e \)
How is weight related to spring extension?
\( mg = k e \)
What happens to energy in a damped system?
It is lost as heat or sound, reducing total mechanical energy.
What is \( k \) in SHM formulas?
Force constant or spring constant (N/m)
What is \( \omega \) in SHM?
Angular velocity (rad/s)
What does \( A \) represent?
Amplitude of motion (meters)
What is the SI unit of energy?
Joule (J)
What is \( e \) in spring motion?
Extension of the spring (m)
Hooke’s Law formula?
\( F = -kx \)
Velocity at any point in SHM?
\( v = \omega \sqrt{A^2 - x^2} \)
Kinetic energy in SHM?
\( KE = \frac{1}{2} m v^2 \)
Potential energy in SHM?
\( PE = \frac{1}{2} k x^2 \)
Total mechanical energy in SHM?
Constant, \( E = \frac{1}{2} k A^2 \)
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