A body is oscillating in simple harmonic motion according to the equation $x=6 \cos \left(2 \pi t+\frac{\pi}{3}\right) \mathrm{m}$. The magnitude of the acceleration (in $\mathrm{m} / \mathrm{s}^2$ ) of the body at $t=\mathrm{ls}$

A particle is exhibiting simple harmonic motion has its displacement $x$ and velocity $v$ related as $4 v^2=25-x^2$. The time period of SHM is

Three masses $700 \mathrm{~g}, 500 \mathrm{~g}$ and 400 g are suspended at the end of a spring shown in figure and are in equilibrium. When the 700 g mass is removed, the system oscillates with a time period of 3 s . If 500 g mass is further removed, then it will oscillate with a period of

A stiff spring having spring constant $k=400 \mathrm{~N} / \mathrm{m}$ is attached to the floor vertically. A mass $m=10 \mathrm{~kg}$ is placed on top of the spring. The block oscillates if it is pressed downward and released. Find the extension in the spring at which the block loses contact with spring. (Take, $g=10 \mathrm{~m} / \mathrm{s}^2$ )