$A$ clock $S$ is based on the oscillation of a spring,and a clock $P$ is based on pendulum motion. Both clocks run at the same rate on Earth. On a planet having the same density as Earth but twice the radius,which of the following is true?

Due to some force $F_1$,a body oscillates with a period of $4/5 \, s$,and due to another force $F_2$,it oscillates with a period of $3/5 \, s$. If both forces act simultaneously,the new period will be .... $s$.

$A$ mass of $5\, {kg}$ is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. $A$ simple pendulum of length $4\, {m}$ has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed? (In ${m} / {s}^{2}$)

Two particles are in $SHM$ in a straight line. Amplitude $A$ and time period $T$ of both the particles are equal. At time $t=0$,one particle is at displacement $y_1 = +A$ and the other at $y_2 = -A/2$,and they are approaching towards each other. After what time do they cross each other?

$A$ particle is executing $SHM$ with an amplitude $A$ and angular frequency $\omega$. The ratio of the maximum acceleration to the maximum velocity of the particle is:

Two identical balls $A$ and $B$,each of mass $0.1 \ kg$,are attached to two identical massless springs. The spring-mass system is constrained to move inside a rigid smooth pipe bent in the form of a circle as shown in the figure. The pipe is fixed in a horizontal plane. The centers of the balls can move in a circle of radius $0.06 \ m$. Each spring has a natural length of $0.06\pi \ m$ and a force constant of $0.1 \ N/m$. Initially,both balls are displaced by an angle $\theta = \pi/6$ radian with respect to the diameter $PQ$ of the circle and released from rest. The frequency of oscillation of the ball $B$ is: