A steady force of $120\ N$ is required to push a boat of mass $700\ kg$ through water at a constant speed of $1\ m/s$ . If the boat is fastened by a spring and held at $2\ m$ from the equilibrium position by a force of $450\ N$ , find the angular frequency of damped $SHM$ ..... $rad/s$
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
A mass $M$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes simple harmonic oscillations with a time period $T$. If the mass is increased by m then the time period becomes $\left( {\frac{5}{4}T} \right)$. The ratio of $\frac{m}{{M}}$ is
The mass $M$ shown in the figure oscillates in simple harmonic motion with amplitude $A$. The amplitude of the point $P$ is
A body of mass $m$ is attached to one end of a massless spring which is suspended vertically from a fixed point. The mass is held in hand, so that the spring is neither stretched nor compressed. Suddenly the support of the hand is removed. The lowest position attained by the mass during oscillation is $4\,cm$ below the point, where it was held in hand.
$(a)$ What is the amplitude of oscillation ?
$(b)$ Find the frequency of oscillation.