Simple Harmonic Motion (SHM) Velocity and Acceleration Quiz

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What is the equation for displacement in Simple Harmonic Motion (SHM)?

$x(t) = A\cos(\omega t)$ (correct)
$x(t) = -\omega^2 A\cos(\omega t)$
$x(t) = -\omega A\sin(\omega t)$
$x(t) = \omega^2 A\cos(\omega t)$

What is the equation for velocity in Simple Harmonic Motion (SHM)?

$v(t) = A\cos(\omega t)$
$v(t) = -\omega A\sin(\omega t)$ (correct)
$v(t) = -A\sin(\omega t)$
$v(t) = \omega A\cos(\omega t)$

What is the equation for acceleration in Simple Harmonic Motion (SHM)?

$a(t) = \omega^2 x(t)$
$a(t) = -A\sin(\omega t)$
$a(t) = -\omega^2 x(t)$ (correct)
$a(t) = \omega^2 A\cos(\omega t)$

What does the minus sign in the restoring force equation indicate?

The direction of the restoring force is always opposite to the displacement. (A) Signup and view all the answers

What does a larger spring constant ($k$) indicate in a spring-mass system?

Higher stiffness and higher frequency of oscillation. (A) Signup and view all the answers

What is the relationship between the spring constant ($k$) and the frequency of oscillation in a spring-mass system?

The larger the spring constant, the higher the frequency of oscillation (A) Signup and view all the answers

In Simple Harmonic Motion (SHM), what does the equation for displacement, $x(t) = A ext{cos}( heta t)$, represent?

The position of the particle at time $t$ in terms of amplitude and angular frequency (A) Signup and view all the answers

What is the relationship between velocity and displacement in Simple Harmonic Motion (SHM)?

Velocity is maximum when displacement is zero (C) Signup and view all the answers

What does the restoring force equation, $F = -kx$, indicate about the force in a spring-mass system?

The force is always directed opposite to the displacement (B) Signup and view all the answers

What does an increase in angular frequency ($ heta$) indicate about a simple harmonic oscillator?

The oscillator has a higher frequency of oscillation (D) Signup and view all the answers

Displacement in SHM (x(t))

The position of the particle at time t in terms of amplitude (A) and angular frequency (ω).

Velocity in SHM (v(t))

The rate of change of displacement, given by the derivative of the displacement equation. It's maximum when displacement is zero.

Acceleration in SHM (a(t))

The rate of change of velocity, given by the derivative of the velocity equation. It's proportional to the displacement and always acts opposite to it.

Restoring Force in SHM (F)

The force that always acts opposite to the displacement, trying to restore the object to its equilibrium position. Proportional to the displacement and the spring constant.