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What is Simple Harmonic Motion (SHM)?
SHM is a type of periodic motion where an object moves back and forth around an equilibrium position.
What are the characteristics of SHM?
Key characteristics include a restoring force proportional to the displacement from equilibrium and motion that is sinusoidal in nature.
What is the formula for displacement in SHM?
The displacement x(t) can be described by the equation: x(t) = A cos(ωt + φ), where A is amplitude, ω is angular frequency, and φ is the phase constant.
What is amplitude in SHM?
Amplitude is the maximum displacement of the object from its equilibrium position.
What is angular frequency in SHM?
Angular frequency (ω) is defined as ω = 2π/T, where T is the period of the motion.
What is the period of SHM?
The period (T) is the time taken for one complete cycle of motion.
What is the relationship between mass and SHM?
In a mass-spring system, the mass affects the period of oscillation; greater mass results in a longer period.
What is the restoring force in SHM?
The restoring force is the force that opposes displacement and is directly proportional to the displacement.
How does energy behave in SHM?
Energy in SHM oscillates between kinetic energy and potential energy, maintaining a constant total mechanical energy.
What is an example of SHM in everyday life?
A common example of SHM is a pendulum swinging back and forth or a mass attached to a spring.
What is the definition of Simple Harmonic Motion (SHM)?
SHM is a periodic motion where the restoring force is directly proportional to the displacement and acts in the opposite direction.
What creates SHM?
SHM is created by a restoring force that is proportional to the negative of the displacement.
What are common examples of SHM?
Common examples include springs, pendulums, and tuning forks.
What is phase in SHM?
Phase refers to the position of the oscillating object in its cycle at a particular time, often measured in radians.
What does the term 'frequency' mean in SHM?
Frequency is the number of oscillations or cycles per unit time, typically measured in Hertz (Hz).
What is the relationship between frequency and period in SHM?
Frequency (f) is the inverse of the period (T): f = 1/T.
What is the maximum speed in SHM?
The maximum speed of an object in SHM occurs at the equilibrium position and is given by v_max = Aω.
What happens to energy in SHM at maximum displacement?
At maximum displacement, the potential energy is at its peak while kinetic energy is zero.
What is the mechanical energy in SHM?
Mechanical energy in SHM remains constant and is the sum of kinetic and potential energy.
What determines the period of a simple pendulum?
The period of a simple pendulum is determined by its length and gravity: T = 2π√(L/g).
What is Damping in SHM?
Damping is the reduction in amplitude of SHM due to external forces, like friction or air resistance.
What is driven harmonic motion?
Driven harmonic motion occurs when an external force drives the oscillation of a system.
What is resonance in SHM?
Resonance is the phenomenon that occurs when an external force matches the natural frequency of the system, amplifying motion.
What is the difference between SHM and general periodic motion?
SHM specifically involves a restoring force proportional to displacement, while general periodic motion may not have this characteristic.
How is the acceleration calculated in SHM?
Acceleration in SHM is calculated using a = -ω²x, where x is the displacement.
What is the significance of amplitude in SHM?
Amplitude represents the maximum extent of displacement from the mean position in SHM.
Can SHM occur in systems without mass?
SHM requires a mass to experience the restoring force; thus, it cannot occur without mass.
What is the effect of increasing amplitude on SHM?
Increasing amplitude increases the maximum speed and total energy but does not affect the period.
How does position affect velocity in SHM?
The velocity in SHM is maximum at the equilibrium position and zero at maximum displacement.
What is the role of springs in SHM?
Springs provide a restoring force that enables simple harmonic motion through Hooke's Law.
