Tag: free, forced and damped oscillations

Questions Related to free, forced and damped oscillations

Two point masses $m _1$ and $m _2$ are coupled by a spring of spring. Constant $k$ and uncompressed length $L _0$. The spring is fully compressed and a thread ties the masses together with negligible separation between them. The tied assembly is moving in the $+x$ direction with uniform speed $v _0$. At a time, say $t = 0$, it is passing the origin and at that instant the thread breaks. The masses, attached to the spring, start oscillating. The displacement of mass $m _1$ given by $x _1(t) = v _0 t(1 - cos \omega t)$ where $A$ is a constant. Find (i) the displacement $x _2(t)$ is $m _2$, and (ii) the relationship between $A$ and $L _0$.

physics oscillations introduction to sound free, forced and damped oscillations resonance

  1. (i) $v _0 t + \dfrac{m _1}{2m _2}A(1 - cos \omega t)$

    (ii) $A = \left(\dfrac{m _2}{2m _1 + m _2}\right)$

  2. (i) $v _0 t + \dfrac{m _1}{m _2}A(1 - cos \omega t)$

    (ii) $A = \left(\dfrac{m _2}{m _1 + m _2}\right)$

  3. (i) $v _0 t + \dfrac{m _1}{3m _2}A(1 - cos \omega t)$

    (ii) $A = \left(\dfrac{m _2}{3m _1 + m _2}\right)$

  4. (i) $v _0 t + \dfrac{m _1}{4m _2}A(1 - cos \omega t)$

    (ii) $A = \left(\dfrac{m _2}{4m _1 + m _2}\right)$

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Correct Option: B

To and fro motion of a particle about its mean position is called -

physics propagation of sound waves introduction to sound free, forced and damped oscillations resonance

  1. frequency

  2. amplitude

  3. vibration

  4. acceleration

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Correct Option: C
Explanation:

To and fro motion of a particle about mean position is called vibrational motion.

The time taken by a vibrating body to complete one vibration is called its frequency. True or false.

physics propagation of sound waves introduction to sound free, forced and damped oscillations resonance

  1. True

  2. False

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Correct Option: B
Explanation:

The time taken by vibrating body to complete one vibration is called time period. so our given statement is false.