Simple Harmonic Motion (SHM) is a type of periodic oscillatory motion where the restoring force acting on a system is directly proportional to its displacement from the equilibrium position and is always directed towards it. For example, in a mass-spring system, when the mass is displaced, the spring exerts a restoring force given by Hooke's Law, F = -kx, where k is the spring constant. This motion is characterized by key parameters such as amplitude (maximum displacement), time period (time for one complete vibration), frequency (vibrations per second), and angular frequency (ω = 2πf ). The displacement over time follows a sinusoidal pattern, making SHM fundamental in understanding waves and vibrations in physics.
What is Simple Harmonic Motion (SHM)?
SHM is a type of periodic oscillatory motion in which the restoring force is directly proportional to the displacement from the equilibrium position and acts in the opposite direction.
What role does Hooke’s Law play in SHM?
Hooke’s Law provides the relationship 𝐹=−𝑘𝑥, which defines the restoring force in systems like a spring, laying the foundation for SHM.
What is amplitude in SHM?
Amplitude is the maximum displacement of the oscillating body from its equilibrium position.
What is the significance of the sine curve in SHM?
The sine curve represents the variation of displacement with time in SHM, showing that the motion is periodic and oscillatory.
What are the key characteristics of acceleration in SHM?
In SHM, acceleration is directly proportional to displacement (𝑎 ∝ −𝑥), always directed towards the mean position, and has a maximum value at the extreme positions.
Which of the following best defines Simple Harmonic Motion (SHM)?
a) Motion with constant velocity
b) Oscillatory motion with restoring force proportional to displacement
c) Random motion of particles
d) Motion along a circular path
Answer: b) Oscillatory motion with restoring force proportional to displacement
What does the negative sign in 𝐹 = − 𝑘 𝑥 represent?
a) The force is constant
b) The force is in the opposite direction to displacement
c) The displacement is zero
d) The motion is uniform
Answer: b) The force is in the opposite direction to displacement
What is the unit of angular frequency (𝜔) in SHM?
a) Seconds
b) Hertz (Hz)
c) Radians per second (rad/s)
d) Meters per second (m/s)
Answer: c) Radians per second (rad/s)
The maximum displacement of an oscillating body from its mean position is called:
a) Frequency
b) Amplitude
c) Time period
d) Angular velocity
Answer: b) Amplitude
In SHM, the acceleration of the body is:
a) Constant in magnitude and direction
b) Proportional to displacement and directed towards the mean position
c) Independent of displacement
d) Always zero
Answer: b) Proportional to displacement and directed towards the mean position