The frequency of oscillations of a mass $m$ connected horizontally by a spring of spring constant $k$ is $4 \ Hz$. When the spring is replaced by two identical springs connected in series as shown in the figure,the effective frequency is:

$A$ body of mass $1 \ kg$ is suspended from a spring of force constant $600 \ N \ m^{-1}$. Another body of mass $0.5 \ kg$ moving vertically upwards hits the suspended body with a velocity of $3 \ m \ s^{-1}$ and gets embedded in it. The amplitude of motion is (in $cm$)

The mass $M$ shown in the figure oscillates in simple harmonic motion with amplitude $A$. The amplitude of the point $P$ is

$A$ particle of mass $m$ is attached to one end of a massless spring of force constant $k$,lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time $t=0$ with an initial velocity $u_0$. When the speed of the particle is $0.5 u_0$,it collides elastically with a rigid wall. After this collision:
$(A)$ the speed of the particle when it returns to its equilibrium position is $u_0$.
$(B)$ the time at which the particle passes through the equilibrium position for the first time is $t=\pi \sqrt{\frac{m}{k}}$.
$(C)$ the time at which the maximum compression of the spring occurs is $t =\frac{4 \pi}{3} \sqrt{\frac{m}{k}}$.
$(D)$ the time at which the particle passes through the equilibrium position for the second time is $t=\frac{5 \pi}{3} \sqrt{\frac{m}{k}}$.

Which type of spring has fast oscillations: stiff or soft?

$A$ block of mass $m$ is attached to two springs of spring constants $k_1$ and $k_2$ as shown in the figure. The block is displaced by $x$ towards the right and released. The velocity of the block when it is at $x/2$ will be