Oscillations — Practice

Question 1

A particle in SHM has amplitude 5 cm and period 2 s. Find the maximum velocity and acceleration.

Accepted Answer

omega = 2 pi/T = pi rad/s. v_max = A omega = 0.05 pi = 0.157 m/s. a_max = A omega^2 = 0.05 pi^2 = 0.493 m/s^2.

Question 2

At what displacement is the kinetic energy equal to the potential energy in SHM?

Accepted Answer

K = U gives (A^2 - x^2) = x^2, so 2x^2 = A^2 and x = +/- A/sqrt(2).

Question 3

A spring of constant 100 N/m carries a 4 kg mass. Find the period.

Accepted Answer

T = 2 pi sqrt(m/k) = 2 pi sqrt(4/100) = 2 pi x 0.2 = 1.257 s.

Question 4

A pendulum clock runs slow. Should the pendulum be lengthened or shortened?

Accepted Answer

Running slow means the period is too long. Since T = 2 pi sqrt(L/g), shorten the pendulum to reduce the period.

Question 5

What is the difference between damped and forced oscillations?

Accepted Answer

In damped oscillations the amplitude decreases over time due to energy loss (friction/drag). In forced oscillations an external periodic force drives the system, and the amplitude depends on the driving frequency, peaking at resonance.

Practice — Oscillations

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