Simple Harmonic Motion and Springs

Flashcards covering the key concepts and formulas related to simple harmonic motion and springs, based on lecture notes.

What is the period (T) of a cyclic system that is vibrating or rotating?

The time required for the system to complete one full cycle.

What is the relationship between frequency (f) and period (T)?

f = 1/T

What is the unit of frequency?

Hertz (Hz), where one cycle/s is one hertz.

Define displacement in the context of vibratory motion.

The distance of the vibrating object from its equilibrium position.

What is the amplitude of vibratory motion?

The maximum displacement from the equilibrium position.

What is a restoring force?

A force that opposes the displacement of the system and is directed toward the equilibrium position.

What is Simple Harmonic Motion (SHM)?

Vibratory motion that a system obeying Hooke's Law undergoes, characterized by a single constant frequency.

What is a Hookean system?

A system that returns to its original configuration after being distorted and released and obeys Hooke's Law.

State Hooke's Law.

F = -kx, where F is the restoring force, k is the spring constant, and x is the displacement.

What does the minus sign in Hooke's Law indicate?

The restoring force is always opposite in direction to the displacement.

What are the units of the spring constant k?

N/m (Newtons per meter)

What is the formula for elastic potential energy (PE) stored in a Hookean spring?

PE = ½kx²

Describe the energy interchange in a vibrating system.

Kinetic energy (KE) and potential energy (PE) are constantly interchanged. At equilibrium, KE is maximum and PE is zero. At maximum displacement, KE is zero and PE is maximum.

What is the formula relating KE and PE in a vibrating spring system?

½mv² + ½kx² = ½kx₀², where x₀ is the amplitude.

How is speed determined in SHM using energy considerations?

|v| = √(k/m) * √(x₀² - x²)

How is acceleration determined in SHM?

a = -(k/m)x

Explain the concept of a reference circle in SHM.

A point moving with constant speed around a circle, where the projection of the point on the x-axis demonstrates SHM.

What is the formula for Vx in terms of the reference circle?

Vx = -vo sin θ

What is the formula for the period T of SHM in terms of m and k?

T = 2π√(m/k)

What is the relationship between acceleration and period in SHM?

a = -(4π²/T²)x

What is the formula for the period of a simple pendulum?

T = 2π√(L/g)

How is SHM expressed in analytic form?

x = x₀ cos(2πft) = x₀ cos(ωt) and y = x₀ sin(2πft) = x₀ sin(ωt)

How do you calculate the angular frequency?

ω = 2πf