Skip to content

Spring Oscillations Viva Questions

What is spring constant or spring factor?

1)         Restoring force per unit displacement (resistance offered by a spring when it is oscillated)

2)        Spring constant is a measure of how stiff a spring is or how much force is needed to stretch or compress it. (Physical significance of spring contact)

Greater the spring factor-> Greater the stiffness-> Greater the torque required

What is parallax error?

Parallax error is a human error that occurs when you read a measuring scale or gauge from an angle, rather than perpendicular to it.

What is angular velocity?

Angular velocity of an object is the object’s angular displacement with respect to time, angular velocity is expressed as follows:

    \[\omega = \frac{d\theta}{dt}\]

What is angular S.H.M.(or simple harmonic motion)?

Angular SHM is a type of oscillatory motion where the torque acting on a body is directly proportional to the angular displacement from its equilibrium position.

What is angular acceleration?

It is defined as the time rate of change of angular velocity.

    \[\alpha = \frac{d\omega}{dt}\]

Difference between angular velocity and angular speed.

Angular velocity is a vector quantity that describes both the magnitude and direction of a rotating object whereas angular speed is a scalar quantity that describes the magnitude of a rotating object.

 Why it is horizontal?

If θ=90o, then sin θ is maximum, then torque will be maximum. It is easy to count number of oscillations because of maximum torque.

What is the daily life use of spring oscillations?

Used in cars to absorb bumps, utilized in pens for the click mechanism, applied in clocks to keep time etc.

Derivation of different terms involved in Spring Oscillations Experiment
Derivation of

    \[I \frac{d^2 \theta}{dt^2} = -k(l\theta) l\]

We know torque \tau = I \alpha = r \times F

Let r = l

We also know F = -kx and \theta = \frac{\text{arc length}}{\text{radius}}

Therefore, since we have assumed r = l, x = l \theta

Substituting these values, we get:

    \[ I \frac{d^2 \theta}{dt^2} = -k(l \theta)l \]

Derivation of

    \[ \omega = \left( \frac{kl^2}{I} \right)^{1/2} \]

We know: \frac{1}{2} mv^2 = \frac{1}{2} kx^2

Therefore, \frac{k}{m} = \frac{v^2}{x^2}

Let x = r

And: v = r\omega \Rightarrow \frac{v}{r} = \omega

Therefore, \omega^2 = \frac{k}{m}

Thus: \omega = \sqrt{\frac{k}{m}}

We also know, moment of inertia: I = mr^2 \Rightarrow m = \frac{I}{r^2}

Therefore, substituting mass from the above equation and assuming r = l, we get:

    \[ \omega = \sqrt{\frac{kl^2}{I}} \]

You can view the full experiment by clicking here.

Tags:

Leave a Reply

Your email address will not be published. Required fields are marked *