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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 .... $s$
A particle of mass $1\, {kg}$ is hanging from a spring of force constant $100\, {Nm}^{-1 .}$ The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period ${T}$. The time when the kinetic energy and potential energy of the system will become equal, is $\frac{{T}}{{x}}$. The value of ${x}$ is ..... .
A particle of mass $m$ executes simple harmonic motion with amplitude $a$ and frequency $v$. The average kinetic energy during its motion from the position of equilibrium to the end is
A block of mass $m$ is suspended separately by two different springs have time period $t_1$ and $t_2$ . If same mass is connected to parallel combination of both springs, then its time period will be
Time period of a simple pendulum in a stationary lift is ' $T$ '. If the lift accelerates with $\frac{ g }{6}$ vertically upwards then the time period will be .....