Simple Harmonic Motion (HL)

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In simple harmonic motion, what characterizes the relationship between acceleration (a) and displacement (x)?

a is inversely proportional to x and in the opposite direction.
a is directly proportional to x and in the same direction.
a is directly proportional to the square of x.
a is directly proportional to x and in the opposite direction. (correct)

A mass-spring system oscillates with a certain period. If the mass is quadrupled, what happens to the period of oscillation?

The period is doubled. (correct)
The period is quadrupled.
The period remains the same.
The period is halved.

A simple pendulum is moved from Earth to a planet where the acceleration due to gravity is four times that of Earth. What is the effect on the period of the pendulum?

The period is halved. (correct)
The period remains the same.
The period is doubled.
The period is quadrupled.

For a mass undergoing simple harmonic motion, at which point in the cycle is the potential energy maximum, assuming the equilibrium position has zero potential energy?

At maximum displacement from the equilibrium position. (A) Signup and view all the answers

What is the phase difference between displacement and velocity in simple harmonic motion?

$\frac{\pi}{2}$ radians (B) Signup and view all the answers

An object undergoes simple harmonic motion. If the amplitude is doubled, how does the total energy of the system change?

The total energy is quadrupled. (C) Signup and view all the answers

A particle oscillates with simple harmonic motion described by $x = x_0 \sin(\omega t + \phi)$. What does $\phi$ represent in this equation?

The phase constant or initial phase. (B) Signup and view all the answers

In a simple harmonic oscillator, at what point is the kinetic energy equal to the potential energy?

At displacement equal to $\frac{x_0}{\sqrt{2}}$ (D) Signup and view all the answers

If the frequency of a simple harmonic oscillator is doubled, how is the angular frequency affected?

It is doubled. (A) Signup and view all the answers

A simple pendulum's length is increased. What effect does this have on the pendulum's frequency?

The frequency decreases. (C) Signup and view all the answers

When does maximum speed occur for a mass undergoing simple harmonic motion?

At the equilibrium position. (B) Signup and view all the answers

What condition is necessary for an object's motion to be classified as simple harmonic?

The restoring force must be proportional to the displacement. (A) Signup and view all the answers

How does the period of a simple pendulum change if its mass is doubled, assuming length and gravitational acceleration remain constant?

The period remains unchanged. (C) Signup and view all the answers

A mass on a spring is oscillating vertically. If the spring constant is increased, how does the period of oscillation change?

The period decreases. (D) Signup and view all the answers

What is the relationship between the total energy ($E_T$), maximum kinetic energy ($E_{Kmax}$), and maximum potential energy ($E_{Pmax}$) in a simple harmonic oscillator?

$E_T = E_{Kmax} = E_{Pmax}$ (A) Signup and view all the answers

The displacement of a particle in SHM is given by $x = A\sin(\omega t)$. What is the velocity of the particle as a function of time?

$v = A\omega \cos(\omega t)$ (A) Signup and view all the answers

The equation for the period of a simple pendulum is $T = 2\pi\sqrt{\frac{L}{g}}$. Which of the following changes will cause the greatest increase in the period?

Halving the acceleration due to gravity (B) Signup and view all the answers

If the displacement of an object in simple harmonic motion is described by $x(t) = A \cos(\omega t)$, what is the acceleration $a(t)$?

$a(t) = -A\omega^2 \cos(\omega t)$ (D) Signup and view all the answers

A mass oscillates on a spring with a period of $T$. If both the mass and the spring constant are doubled, what is the new period?

$T$ (B) Signup and view all the answers

Consider a mass-spring system oscillating horizontally. At what point in the oscillation is the magnitude of the net force on the mass the greatest?

When the mass is at its maximum displacement from equilibrium. (C) Signup and view all the answers

What happens to the maximum velocity of an object in simple harmonic motion if the amplitude is doubled and the angular frequency remains constant?

It doubles (A) Signup and view all the answers

A simple pendulum is oscillating with a small angle. If you increase its initial angular displacement (but still keep it small), which of the following will increase?

Maximum velocity (B) Signup and view all the answers

How does the average speed of a mass undergoing SHM during one full oscillation relate to its maximum speed $v_{max}$?

The average speed is zero (A) Signup and view all the answers

A mass on a spring is displaced from its equilibrium position and released. Which of the following is true as the mass passes through the equilibrium position?

The potential energy is minimum and the kinetic energy is maximum. (D) Signup and view all the answers

If a simple harmonic oscillator's total energy is increased, and the spring constant and mass remain unchanged, what must also increase?

Amplitude (B) Signup and view all the answers

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What is oscillation?

Back and forth movement of an object.

What is simple harmonic motion (SHM)?

Motion where restoring force is proportional to the displacement.