Simple Harmonic Motion Quiz

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What is the condition for maximum velocity in simple harmonic motion?

Occurs when the position is maximum
Occurs when the mass is at rest
Occurs when acceleration is zero (correct)
Occurs at equilibrium position

Which of the following describes the acceleration at maximum displacement in simple harmonic motion?

It is maximum and directed away from equilibrium
It varies unpredictably at maximum displacement
It is maximum and directed towards equilibrium (correct)
It is zero at maximum displacement

In the equations provided for simple harmonic motion, what does $rac{d^2x}{dt^2}$ represent?

The acceleration of the mass (correct)
The velocity of the mass
The maximum velocity of the system
The force acting on the mass

What is the relationship between angular frequency $eta$ and spring constant $k$ as stated in the equations?

$eta = rac{k}{m}$ (C) Signup and view all the answers

If the amplitude $A$ is doubled in an SHM system, what happens to the maximum acceleration?

It quadruples (B) Signup and view all the answers

What is the correct relationship between period and frequency?

The period is the inverse of frequency. (D) Signup and view all the answers

If the mass of a particle undergoing simple harmonic motion is doubled while keeping the force constant the same, what happens to the frequency?

Decreases by a factor of √2. (D) Signup and view all the answers

Which formula correctly defines frequency in relation to the angular frequency?

f = ω/2π (C) Signup and view all the answers

Which of the following statements about the period and frequency is true?

Higher spring stiffness results in a higher frequency. (C) Signup and view all the answers

What would be the effect on period if the spring constant is halved while keeping the mass constant?

The period would increase. (D), The period would also be halved. (B) Signup and view all the answers

What is the relationship between total mechanical energy and amplitude in a simple harmonic oscillator?

Total mechanical energy is constant and proportional to the square of the amplitude. (A) Signup and view all the answers

At the equilibrium position of a simple harmonic oscillator, which of the following statements is true?

Kinetic energy is maximum and potential energy is zero. (A) Signup and view all the answers

Using the expression for total mechanical energy, when is the potential energy at its maximum?

When the oscillator is at maximum displacement. (B) Signup and view all the answers

Which formula correctly calculates the kinetic energy at any point in the motion of a simple harmonic oscillator?

K = rac{1}{2}mA^2 imes ext{sin}^2(ωt + φ) (B) Signup and view all the answers

The trigonometric identity used in the expression for total mechanical energy leads to which statement about energy distribution?

The sum of kinetic and potential energy equals the total mechanical energy at all times. (A) Signup and view all the answers

What does the constant A represent in simple harmonic motion?

The maximum displacement from the equilibrium position (C) Signup and view all the answers

How is the angular frequency ω mathematically defined?

ω = √(k/m) (B) Signup and view all the answers

What is the phase constant φ when a particle is at its maximum position x = A at t = 0?

0 (A) Signup and view all the answers

What does the quantity (ωt + φ) represent in the context of simple harmonic motion?

The phase of the motion (D) Signup and view all the answers

What characteristic of the function x(t) reflects its periodic nature?

It is the same each time ωt increases by 2π radians. (C) Signup and view all the answers

Simple Harmonic Oscillator Energy

The total mechanical energy of a simple harmonic oscillator remains constant and depends on the square of its amplitude.

Kinetic Energy (K)

The energy of motion in a simple harmonic oscillator, maximum at equilibrium position.

Potential Energy (U)

Stored energy due to position, maximum at maximum displacement in a simple harmonic oscillator.

Total Mechanical Energy (E)

The sum of kinetic and potential energies in a simple harmonic oscillator, constant throughout the oscillation.