+91-8076753736 [email protected]

-->

Oscillations

Question

Wired Faculty App

The frequency of oscillations of a mass m connected horizontally by a spring of spring constant k is 4 Hz. When the spring is replaced by two identical spring as shown in figure. Then the effective frequency is

4 $\sqrt{2}$

1.5

1.31

2 $\sqrt{2}$

Solution

D.

2 $\sqrt{2}$

If one spring is connected then frequency = 4Hz

4 = $\frac{1}{2 π} \sqrt{\frac{k}{m}}$ ....(i)

If two springs are connected in series, then frequency

v = $\frac{1}{2 π} \sqrt{\frac{k'}{m}}$ ....(ii)

$\{∵ k' = \frac{k}{2}\}$

From equation (i) and (ii)

$\frac{4}{v} = \frac{\frac{1}{2 π} \sqrt{\frac{k}{m}}}{\frac{1}{2 π}} \sqrt{\frac{k}{2 m}}$

$\frac{4}{v} = \sqrt{2}$

v = 2 $\sqrt{2}$ Hz

Some More Questions From Oscillations Chapter

If x, v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time?

The displacement of an object attached to a spring and executing simple harmonic motion is given by x = 2 × 10^-2 cos πt metres. The time at which the maximum speed first occurs

A particle of mass m executes simple harmonic motion with amplitude ‘a’ and frequency ‘ν’. The average kinetic energy during its motion from the position of equilibrium to the end is

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency ω. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

The function sin²(ωt) represents

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation