Simple Harmonic Motion

Simple harmonic motion of a particle can be described as the motion of a particle in which 
 The time period of oscillation of a torsional pendulum of moment of inertia I is
A horizontal spring-block of mass $$2kg$$ executes S.H.M. When the block is passing through its equilibrium position, an object of mass $$1kg$$ is put gently on it and the two move together. The new amplitude of vibration is ( A being its initial amplitude) ?
The amplitude of a damped harmonic oscillator becomes halved in $$\ minute$$. After three minutes, the amplitude will becomes $$\dfrac{1}{x}$$ of initial amplitude, where $$x$$ is ?
A resonance tube is resonated with tuning fork of frequency 256 Hz. If the length of first and second resonating air columns are 32 cm and 100 cm, then end correction will be