Question

The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $T$. If along with it another mass $M$ is also suspended, the period of oscillation will now be

• A. T
• B. $\frac{ T}{ \sqrt 2}$
• C. 2T
• D. $\sqrt 2 T$

Answer 1

Answer: (D)

$\sqrt 2 T$

Answer 2

T is the oscillation period of a mass M hung from a light spring. The period of oscillation will now be if another mass M is suspended alongside it.

F ∝ X

Here, F = Force and X = Displacement

The period T of an oscillating mass M suspended from a light spring. Now, if another mass M is hanging beside it, the period of oscillation will be.

T = 2πM/K

The oscillating mass M's period T, which is hung from a light spring. Now, the period of oscillation will be if another mass M is hanging next to it.

T = 2πM/K

Now when two M masses are there then, M+M = 2M and now the time period is T1

So, T1 = 2π2M/K

T1 = 2 x T = 2T

An oscillatory motion is simple harmonic motion (SHM). According to SHM, a particle's acceleration is shown to be inversely related to its displacement from the initial position at any given point. A specific type of oscillatory motion is known as SHM.

As a result, all simple harmonic movements are capable of having an oscillatory and periodic character. The opposite, however, is untrue. Not every oscillatory motion is an SHM.

Parameters in SHM that are affected by time include displacement, velocity, acceleration, and force. Sinusoids are sometimes referred to as sine, and the cosine functions serve to illustrate this. Simple Harmonic Motion explains the unique properties of alternating currents, sound waves, and light waves.