Simple Harmonic Motion Quiz

False (B)

A force that returns the particle towards its equilibrium position.

<p>displacement</p> Signup and view all the answers

<p>Time period = The time interval after which the motion is repeated. Oscillation = Motion of a body moving to and fro on the same path. Force constant = The constant relating force and displacement in SHM (k). Equilibrium position = The point where resultant force on the particle is zero.</p> Signup and view all the answers

<p>Force is proportional to displacement and acts in the opposite direction. (D)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>sqrt(k/m)</p> Signup and view all the answers

<p>velocity</p> Signup and view all the answers

<p>v = Velocity of the particle w = Angular frequency A = Amplitude of the motion x = Displacement from equilibrium</p> Signup and view all the answers

<p>$U(x) = \frac{1}{2}kx^2$ (D)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>$\frac{1}{2}m\omega^2A^2$</p> Signup and view all the answers

<p>simple harmonic</p> Signup and view all the answers

<p>Potential Energy (U) = $\frac{1}{2}m\omega^2x^2$ Kinetic Energy (K) = $\frac{1}{2}mA^2\omega^2cos^2(\omega t+\delta)$ Total Mechanical Energy (E) = $\frac{1}{2}m\omega^2A^2$ Force (F) = $-kx$</p> Signup and view all the answers

<p>The status of the particle. (D)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>$v = \frac{1}{T}$</p> Signup and view all the answers

<p>phase constant</p> Signup and view all the answers

<p>Time Period (T) = Time taken for one complete oscillation Frequency (v) = Number of oscillations per unit time Angular Frequency (w) = Rate of change of the phase Phase = The status of the particle in SHM</p> Signup and view all the answers

<p>At the positive extreme position. (D)</p> Signup and view all the answers

<p>$w = \sqrt{\frac{k}{m}}$ (C)</p> Signup and view all the answers

<p>$T = 2\pi\sqrt{\frac{m}{k}}$</p> Signup and view all the answers

<p>$\pi/2$ (B)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>$\pi$</p> Signup and view all the answers

<p>constant</p> Signup and view all the answers

<p>Particle at mean position moving towards positive x-direction at t=0 = $\delta = 0$ Particle at positive extreme position at t=0 = $\delta = \pi/2$ Particle at mean position moving towards negative x-direction at t=0 = $\delta = \pi$ Particle at negative extreme position at t=0 = $\delta = 3\pi/2$</p> Signup and view all the answers

<p>The particle's projection onto the x-axis represents simple harmonic motion. (D)</p> Signup and view all the answers

<p>$5\pi/6$ (D)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>The maximum displacement of the oscillating object from its equilibrium position. (B)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>small angle of displacement</p> Signup and view all the answers

<p>phase constant</p> Signup and view all the answers

<p>The period is doubled. (B)</p> Signup and view all the answers

<p>Amplitude = Maximum displacement from equilibrium Period = Time for one complete oscillation Frequency = Number of oscillations per unit time Phase Constant = Initial position of the oscillator</p> Signup and view all the answers

<p>$40\pi$ rad/s (B)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

Type of oscillation where acceleration is proportional to displacement from a fixed point.

The interval after which a motion repeats in harmonic or periodic motion.

The fixed point towards which acceleration in SHM is directed.

The force that pulls the particle back to the equilibrium position in SHM.

A constant representing the stiffness of a spring, related to force and displacement.

A type of periodic motion where a particle moves back and forth around a central point under a restoring force.

The distance and direction from the equilibrium position of a mass in simple harmonic motion.

A measure of how fast something oscillates; defined as w = √(k/m).

The formula relates velocity (v) to displacement (x), expressed as v = w√(A² - x²).

The number of oscillations per unit time, measured in Hertz (Hz).

A term indicating the position of a particle in simple harmonic motion at a given time.

The chosen instant in time from which oscillation measurements start.

The constant in the phase equation which depends on the starting point of time.

When phase is zero, the particle is crossing mean position moving positively.

When phase is π/2, the particle reaches maximum positive position.

Phase changes of 2π, 4π, etc., do not change the state of motion.

Point Q on the X-axis where the perpendicular from P intersects.

Energy stored due to displacement in SHM, U(x) = 1/2 kx².

Energy conserved in SHM, E = 1/2 mw²A², independent of time.

The equation for displacement in simple harmonic motion, expressed as x = A sin(wt + δ).

The position where the particle passes through at t=0, moving in the positive direction.

Phase related to extreme positions; for maximum displacement, δ = π/2.

The concept that SHM can be viewed as the projection of circular motion.

The constant rate at which the particle moves around the circle in circular motion.

The x and y coordinates of a particle in circular motion are expressed as x = A cos(wt) and y = A sin(wt).

The maximum angle of displacement from the vertical for a swing, here θ₀ = π/10 rad.

The time taken for one complete cycle of motion; calculated as T = 2π/w.

An ideal model consisting of a mass on a light string swinging under the influence of gravity.

The vertical position where the pendulum would hang still; corresponds to θ = 0.

The repetitive back-and-forth movement of the pendulum around the equilibrium position.

The fixed circular path that the pendulum's mass follows around the suspension point.