Mass Attached to Spring Lab

• The rest position of mass attached with spring is its mean position or equilibrium position
• By applying external force, mass can be displaced from it mean position
• If the mass is displaced from mean position and applied force is removed, it starts to and fro motion about its mean position
• During this to and fro motion, its kinetic energy is maximum at mean position while zero at extreme positions
• Potential energy is maximum at extreme positions, while it is zero at mean position
• Spring constant is the measure of stiffness of spring. Large value of spring means stiff spring while small values mean soft spring
• The motion of mass attached with spring is simple harmonic motion
• Time period of mass attached with spring is directly proportional to square root of mass and inversely proportional to square root of spring constant

Time Period:

$$ T= 2 \pi \sqrt{\frac{m}{k}} $$

Frequency:

$$ f= \frac{1}{2\pi} \sqrt{\frac{k}{m}} $$

Instantaneous displacement:

$$ v= v_{0} \sqrt{(1- \frac{x^2}{x^2_{0}})}$$

Potential Energy:

$$ P.E= \frac{1}{2}kx^2 $$

Kinetic Energy:

$$ K.E= \frac{1}{2}k(x^2_{0}-x^2) $$