The drawing shows a top view of a frictionless horizontal surface, where there are two indentical springs with particles of mass $m_1$ and $m_2$ attached to them. Each spring has a spring constant of $1200\ N/m.$ The particles are pulled to the right and then released from the positions shown in the drawing. How much time passes before the particles are again side by side for the first time if $m_1 = 3.0\ kg$ and $m_2 = 27 \,kg \,?$
$\frac{\pi}{40}\ sec$
$\frac{\pi}{20}\ sec$
$\frac{3\pi}{40}\ sec$
$\frac{\pi}{10}\ sec$
An assembly of identical spring-mass systems is placed on a smooth horizontal surface as shown. At this instant, the springs are relaxed. The left mass is displaced to the/left and theiright mass is displaced to the right by same distance and released. The resulting collision is elastic. The time period of the oscillations of system is
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 $5\; kg$ collar is attached to a spring of spring constant $500\;N m ^{-1} .$ It slides without friction over a hortzontal rod. The collar is displaced from its equilibrium position by $10.0\; cm$ and released. Calculate
$(a)$ the period of oscillation.
$(b)$ the maximum speed and
$(c)$ maximum acceleration of the collar.
A spring having with a spring constant $1200\; N m ^{-1}$ is mounted on a hortzontal table as shown in Figure A mass of $3 \;kg$ is attached to the free end of the spring. The mass is then pulled sideways to a distance of $2.0 \;cm$ and released. Determine
$(i)$ the frequency of oscillations,
$(ii)$ maximum acceleration of the mass, and
$(iii)$ the maximum speed of the mass.
A mass of $0.2\,kg$ is attached to the lower end of a massless spring of force-constant $200\, N/m,$ the upper end of which is fixed to a rigid support. Which of the following statements is/are true ?