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
- T
- $ \frac{ T}{ \sqrt 2} $
- 2T
- $ \sqrt 2 T $
The Correct Option is D
Approach Solution - 1
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.
Approach Solution -2
We know T= 2𝜋\(\sqrt{\frac{M}{K}}\)
When another mass is suspended
Total mass = M+M = 2M
Then Period, T’ = 2𝜋\(\sqrt{\frac{2M}{K}}\) = √2 2𝜋\(\sqrt{\frac{M}{K}}\) = √2 T
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Concepts Used:
Oscillations
Oscillation is a process of repeating variations of any quantity or measure from its equilibrium value in time . Another definition of oscillation is a periodic variation of a matter between two values or about its central value.
The term vibration is used to describe the mechanical oscillations of an object. However, oscillations also occur in dynamic systems or more accurately in every field of science. Even our heartbeats also creates oscillations. Meanwhile, objects that move to and fro from its equilibrium position are known as oscillators.
Read More: Simple Harmonic Motion
Oscillation- Examples
The tides in the sea and the movement of a simple pendulum of the clock are some of the most common examples of oscillations. Some of examples of oscillations are vibrations caused by the guitar strings or the other instruments having strings are also and etc. The movements caused by oscillations are known as oscillating movements. For example, oscillating movements in a sine wave or a spring when it moves up and down.
The maximum distance covered while taking oscillations is known as the amplitude. The time taken to complete one cycle is known as the time period of the oscillation. The number of oscillating cycles completed in one second is referred to as the frequency which is the reciprocal of the time period.