A man weighing $60\ kg$ stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude $0.1\ m$ and frequency $\frac{2}{\pi } Hz$. Which of the following staements is correct
The spring balance reads the weight of man as $60\ kg$
The spring balance reading fluctuates between $60\ kg$. and $70\ kg$
The spring balance reading fluctuates between $50\ kg$ and $60\ kg$
The spring balance reading fluctuates between $50\ kg$ and $70\ kg$
A mass $m$ is suspended from the two coupled springs connected in series. The force constant for springs are ${K_1}$ and ${K_2}$. The time period of the suspended mass will be
A $2\, Kg$ block moving with $10\, m/s$ strikes a spring of constant $\pi ^2 N/m$ attached to $2\, Kg$ block at rest kept on a smooth floor, the velocity of the rear $2\, kg$ block after it separates from the spring will be ..... $m/s$
A mass attached to a spring is free to oscillate, with angular velocity $\omega,$ in a hortzontal plane without friction or damping. It is pulled to a distance $x_{0}$ and pushed towards the centre with a velocity $v_{ o }$ at time $t=0 .$ Determine the amplitude of the resulting oscillations in terms of the parameters $\omega, x_{0}$ and $v_{ o } .$ [Hint: Start with the equation $x=a \cos (\omega t+\theta)$ and note that the initial velocity is negative.]
For the damped oscillator shown in Figure the mass mof the block is $200\; g , k=90 \;N m ^{-1}$ and the damping constant $b$ is $40 \;g s ^{-1} .$ Calculate
$(a)$ the period of oscillation,
$(b)$ time taken for its amplitude of vibrations to drop to half of Its inittal value, and
$(c)$ the time taken for its mechanical energy to drop to half its initial value.
A spring of force constant $k$ is cut into lengths of ratio $1:2:3$ . They are connected in series and the new force constant is $k'$ . Then they are connected in parallel and force constant is $k''$ . Then $k':k''$ is