In a simple pendulum experiment for the determination of acceleration due to gravity, the error in the measurement of the length of the pendulum is $1 \%$ and the error in the measurement of the time period is $2 \%$. The error in the estimation of acceleration due to gravity is

A massless spring of length $l$ and spring constant $k$ oscillates with a time period $T$ when loaded with a mass $m$. The spring is now cut into three equal parts and are connected in parallel. The frequency of oscillation of the combination when it is loaded with ${ }_{3}$ mass 4 m is

If a body dropped freely from a height of 20 m reaches the surface of a planet with a velocity of $31.4 \mathrm{~ms}^{-1}$. then the length of a simple pendulum that ticks seconds on the planet is

A particle of mass 4 mg is executing simple harmonic motion along $X$-axis with an angular frequency of $40 \mathrm{rad} \mathrm{s}^{-1}$. If the potential energy of the particle is $V(x)=a+b x^2$, where $V(x)$ is in joule and $x$ is in metre, then the value of $b$ is

In a time $t$ amplitude of vibrations of a damped oscillator becomes half of its initial value, then the mechanical energy of the oscillator decreases by

For a particle executing simple harmonic motion, the kinetic energy of the particle at a distance of 4 cm from the mean position is $1 / 3$ rd of the maximum kinetic energy. The amplitude of the motion is