$A$ simple harmonic oscillator consists of a particle of mass $m$ and an ideal spring with spring constant $k$. The particle oscillates with a time period $T$. The spring is cut into two equal parts. If one part oscillates with the same particle,the new time period will be

The force constant of a weightless spring is $16 \, N/m$. $A$ body of mass $1.0 \, kg$ suspended from it is pulled down through $5 \, cm$ and then released. The maximum kinetic energy of the system (spring + body) will be

$A$ body of mass $5\; kg$ hangs from a spring and oscillates with a time period of $2\pi\; s$. If the body is removed,the length of the spring will decrease by:

The vertical extension in a light spring by a weight of $1\, kg$ suspended from the wire is $9.8\, cm$. What is the period of oscillation?

$A$ mass $m$ is suspended from a spring of length $l$ and force constant $K$. The frequency of vibration of the mass is $f_1$. The spring is cut into two equal parts and the same mass is suspended from one of the parts. The new frequency of vibration of the mass is $f_2$. Which of the following relations between the frequencies is correct?

Inside a lift, a spring (force constant $k = 1000 \ N/m$) and a block $(mass = 1 \ kg)$ are both in a state of rest. Now, the lift suddenly starts moving upwards with an acceleration $a = g$. Find the maximum total compression in the spring in centimeters. $(g = 10 \ m/s^2)$