Different types of oscillations (Free, Damped, Forced Oscillation and Resonance) PYQs: JEE Mains Physics

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1. 1. A block of mass \(1 \,kg\) attached to a spring is made to oscillate with an initial amplitude of \(12\, cm\). After \(2\, minutes\) the amplitude decreases to \(6\, cm\). Determine the value of the damping constant for this motion. (take In \(2=0.693\) ) 2021 Hard
2. 2. Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass \(=500\, g\), Decay constant \(=20 \,g / s\) then ...... \(s\) time is required for the amplitude of the system to drop to half of its initial value ? \((\ln 2=0.693)\) 2021 Hard
3. 3. A \(LCR\) circuit behaves like a damped harmonic oscillator. Comparing it with a physical springmass damped oscillator having damping constant \(\mathrm{b}\), the correct equivalence would be: 2020 Hard
4. 4. A damped harmonic oscillator has a frequency of \(5\) oscillations per second. The amplitude drops to half its value for every \(10\) oscillations. The time it will take to drop to \(\frac{1}{1000}\) of the original amplitude is close to .... \(s\) 2019 Hard
5. 5. The displacement of a damped harmonic oscillator is given by \(x\left( t \right) = {e^{ - 0.1\,t}}\,\cos \left( {10\pi t + \varphi } \right)\)  The time taken for its amplitude of vibration to drop to half of its initial value is close to .... \(s\) 2019 Medium
6. 6. The angular frequency of the damped oscillator is given by, \(\omega  = \sqrt {\left( {\frac{k}{m} - \frac{{{r^2}}}{{4{m^2}}}} \right)} \) where \(k\) is the spring constant, \(m\) is the mass of the oscillator and \(r\) is the damping constant. If the ratio \(\frac{{{r^2}}}{{mk}}\) is \(8\%\), the change in time period compared to the undamped oscillator is approximately as follows 2014 Medium
7. 7. The amplitude of a damped oscillator decreases to \(0.9\) times its original magnitude in \(5\ s\). In another \(10\ s\) it will decrease to \(\alpha \) times its original magnitude, where  \(\alpha \) equals 2013 Medium

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