Simple Harmonic Motion is a type of periodic motion where an object oscillates back and forth through an equilibrium position, and the restoring force is proportional to the displacement.
What is the formula for the period of a mass-spring system in SHM?
The period T is given by T = 2π√(m/k), where m is the mass and k is the spring constant.
Define the amplitude of SHM.
Amplitude is the maximum displacement of the object from its equilibrium position in SHM.
What is the relationship between frequency and period in SHM?
The frequency f is the reciprocal of the period T, that is, f = 1/T.
Explain the concept of phase in SHM.
The phase of SHM describes the position and direction of motion of the oscillating object at a given time.
How is energy conserved in SHM?
In SHM, mechanical energy is conserved, oscillating between kinetic and potential energy.
What is the role of damping in SHM?
Damping reduces the amplitude of SHM over time due to non-conservative forces like friction.
Describe the motion of a simple pendulum in SHM.
A simple pendulum exhibits SHM when the angle of displacement is small. It swings back and forth through its equilibrium position.
What is the natural frequency of a system in SHM?
The natural frequency is the frequency at which a system oscillates when not subjected to a continuous or repeated external force.
Can you give an example of a real-world application of SHM?
One example is the use of SHM in the design of tuning forks, which produce a consistent pitch when struck.
What is the equation of motion for SHM?
The motion equation is x(t) = A cos(ωt + φ), where A is amplitude, ω is angular frequency, t is time, and φ is phase.
What influences the angular frequency in SHM?
Angular frequency ω is influenced by the mass and stiffness (spring constant) of the system, ω = √(k/m).
What is resonance in the context of SHM?
Resonance occurs when a system is driven at its natural frequency, leading to a large increase in amplitude.
How does the length of a pendulum affect its period in SHM?
The period T of a pendulum is proportional to the square root of its length, T = 2π√(l/g).
Why is SHM considered a foundational concept in physics?
SHM is foundational because it models the behavior of waves and oscillations, applicable to various physical systems and technologies.