JEE Main Ultimate Online Test Series - 2027
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A spring stretches by 2 mm when it is loaded with a mass of 200 g . From equilibrium position the mass is further pulled down by 2 mm and released. The frequency associated with the system and maxmimum energy in the spring are $\_\_\_\_$ Hz and $\_\_\_\_$ J, respectively.
(Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )
A particle is executing simple harmonic motion. Its amplitude is $A$ and time period is 5 sec . The time required by it to move from $x=A$ to $x=\frac{A}{\sqrt{2}}$ is $\_\_\_\_$ sec.
$$ \text { Match List - I with List - II. } $$
| $$ \text { List - I } $$ |
$$ \text { List - II } $$ |
||
|---|---|---|---|
| A. | $$ \sin ^2 \omega t $$ |
I. | Periodic with time period $T=\frac{\pi}{\omega}$ but not simple harmonic motion (SHM) |
| B. | $$ \sin ^3(2 \omega t) $$ |
II. | Periodic with time period $T=\frac{2 \pi}{\omega}$ but Not SHM |
| C. | $$ \sin (\omega t)+\cos (\pi \omega t) $$ |
III. | Periodic with time period $T=\frac{\pi}{\omega}$ and SHM |
| D. | $$ \cos \omega t+\cos 2 \omega t $$ |
IV. | Non-periodic |
Choose the correct answer from the options given below :
A uniform disc of radius $R$ and mass $M$ is free to oscillate about the axis $A$ as shown in the figure. For small oscillations the time period is $\_\_\_\_$ .
(g is acceleration due to gravity)
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