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The displacement of a particle varies according to the relation $x = 3 \ sin\ 100t + 8\ cos^2\ 50t$ . Which of the following is incorrect about this motion
Which of the following expressions corresponds to simple harmonic motion along a straight line, where $x$ is the displacement and $a, b, c$ are positive constants?
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 .... $s$
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
A particle of mass $m$ is performing linear simple harmonic motion. Its equilibrium is at $x = 0,$ force constant is $K$ and amplitude of $SHM$ is $A$. The maximum power supplied by the restoring force to the particle during $SHM$ will be
A spring of force constant $k$ is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force constant of
Two pendulums begins to swing simultaneously. The first pendulum makes $11$ full oscillations when the other makes $9$. The ratio of length of the two pendulums is