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A mass $\mathrm{m}$ is suspended from a spring of negligible mass and the system oscillates with a frequency $f_1$. The frequency of oscillations if a mass $9 \mathrm{~m}$ is suspended from the same spring is $f_2$. The value of $\frac{f_1}{f_{.2}}$ is_____________.
In figure $(A),$ mass ' $2 m$ ' is fixed on mass ' $m$ ' which is attached to two springs of spring constant $k$. In figure $(B),$ mass ' $m$ ' is attached to two spring of spring constant ' $k$ ' and ' $2 k$ '. If mass ' $m$ ' in $(A)$ and $(B)$ are displaced by distance ' $x$ ' horizontally and then released, then time period $T_{1}$ and $T_{2}$ corresponding to $(A)$ and $(B)$ respectively follow the relation.
A particle free to move along the $x-$axis has potential energy given by $U(x) = k[1 - \exp {( - x)^2}]$ for $ - \infty \le x \le + \infty $, where k is a positive constant of appropriate dimensions. Then
An object is attached to the bottom of a light vertical spring and set vibrating. The maximum speed of the object is $15\, cm/sec$ and the period is $628$ milli-seconds. The amplitude of the motion in centimeters is
A point performs simple harmonic oscillation of period $T$ and the equation of motion is given by $x=Asin$$\left( {\omega t + \frac{\pi }{6}} \right)$. After the elapse of what fraction of the time period the velocity of the point will be equal to half of its maximum velocity?
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
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 .....