Simple Harmonic Motion Quiz

What is the primary characteristic of simple harmonic motion (SHM)?

The center of oscillation in SHM is always a point of maximum potential energy.

In the context of simple harmonic motion, what is a 'restoring force'?

The defining equation of SHM, $F = -kx$, indicates that the force is proportional to the ______ and acts in the opposite direction.

Match the following terms related to Simple Harmonic Motion with their corresponding definitions/descriptions:

What is the relationship between the force acting on a particle and its displacement in simple harmonic motion?

In simple harmonic motion, the velocity of the particle is always constant.

A block-spring system oscillates with SHM. If the spring constant is k and the mass of the block is m, what is the angular frequency w of the oscillation?

In simple harmonic motion, when the displacement is at its maximum, the ______ is zero.

Match the following variables with their representation in the equation for velocity in SHM:

In simple harmonic motion, how does the potential energy, $U(x)$, vary with displacement, $x$?

The total mechanical energy in simple harmonic motion changes over time due to the continuous exchange between kinetic and potential energy.

A particle is undergoing simple harmonic motion. If the angular frequency is $\omega$ and the amplitude is A, what is the expression for the total mechanical energy, E, of the particle?

The projection of a uniform circular motion on a diameter of the circle is a _______ _______ motion.

Match the following terms related to simple harmonic motion with their correct expressions:

What does the phase of an object in simple harmonic motion determine?

A phase change of $\pi$ brings a particle in simple harmonic motion to the same status.

What is the relationship between frequency ($v$) and time period (T)?

The constant appearing in the SHM equation is known as the ______.

Match the following terms with their definitions:

If the phase of a particle in SHM is $\frac{\pi}{2}$, where is the particle located?

How does the angular frequency (w) relate to the spring constant (k) and mass (m) in a spring-mass system?

Write the formula for the time period $T$ of a simple harmonic oscillator in terms of mass $m$ and spring constant $k$.

If a particle in simple harmonic motion is at its positive extreme position at $t = 0$, what is the phase constant $\delta$?

The phase constant (\delta) in simple harmonic motion must always be zero.

A particle is undergoing simple harmonic motion. If its displacement is given by $x = A \sin(\omega t + \delta)$, and at $t=0$, $x = 0$ and the velocity is negative, what is the value of the phase constant (\delta)?

The general equation for displacement in simple harmonic motion can be written as $x = A \sin(\omega t + \delta)$, which is equivalent to $x = A \cos(\omega t + \delta')$, where (\delta') is another arbitrary ________.

Match the following scenarios with the appropriate phase constant (\delta) if $x = A \sin(\omega t + \delta):

A particle moves in a circle with radius $A$ at a constant angular speed $\omega$. If its $x$-coordinate is given by $x = A \cos(\omega t)$, what represents the physical interpretation of this?

Given a particle executing simple harmonic motion described by $x = A\sin(\omega t + \delta)$, if at $t = 0$ the particle is at $x = A/2$ and moving in the negative x-direction, what is the correct phase constant (\delta)?

If two simple harmonic motions are being considered together, it is impossible to choose the phase constant of one of them as (\delta = 0).

In the context of simple harmonic motion, what does the term 'amplitude' represent?

A simple pendulum's motion is always perfectly simple harmonic, regardless of the amplitude of its oscillations.

What condition must be met for the motion of a simple pendulum to be considered approximately simple harmonic?

In the equation $θ = θ_0 sin(wt + δ)$, the term 'δ' represents the ______.

A simple pendulum consists of a mass $m$ suspended by a string of length $l$. If the length of the string is quadrupled, how does the period of the pendulum change?

Match the terms with their descriptions related to simple harmonic motion:

Given the equation $θ = \frac{\pi}{10} rad \cdot cos[(40\pi s^{-1})t]$, what is the angular frequency ($w$) of the motion?

In an ideal simple pendulum, the mass of the string is assumed to be a significant factor affecting the pendulum's period.