Questions in Oscillations

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Two springs with spring constants ${{K}_{1}}=1500\,N/m$ and ${{K}_{2}}=3000\,N/m$ are stretched by the same force. The ratio of potential energy stored in spring will be
If a spring extends by $x$ on loading, then energy stored by the spring is (if $T$ is the tension in the spring and $K$ is the spring constant)
A weightless spring of length 60 cm and force constant 200 N/m is kept straight and unstretched on a smooth horizontal table and its ends are rigidly fixed. A mass of 0.25 kg is attached at the middle of the spring and is slightly displaced along the length. The time period of the oscillation of the mass is
The time period of a mass suspended from a spring is $T$. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be
A mass $M$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes S.H.M. of time period $T$. If the mass is increased by $m$, the time period becomes $5T/3$. Then the ratio of $m/M$ is
An object is attached to the bottom of a light vertical spring and set vibrating. The maximum speed of the object is 15 cm/sec and the period is 628 milli-seconds. The amplitude of the motion in centimeters is
When a mass m is attached to a spring, it normally extends by 0.2 m. The mass m is given a slight addition extension and released, then its time period will be
If a body of mass 0.98 kg is made to oscillate on a spring of force constant 4.84 N/m, the angular frequency of the body is
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 mass is ${{f}_{2}}$. Which of the following relations between the frequencies is correct
A mass $m$ oscillates with simple harmonic motion with frequency $f=\frac{\omega }{2\pi }$ and amplitude $A$ on a spring with constant $K$ , therefore

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