Question

lock of mass m2 is attached to a spring of force constant k and m1 . m2. If the system is released from rest, and the spring is initially not stretched or com- pressed, find an expres- sion for the maximum displacement d of m2

Answer 1

Answer:

The maximum displacement of the mass m₂ $= \frac{2(m_1-m_2)g}{k}$

Explanation:

Kinetic Energy (K) = 1/2mv²

Potential Energy (P) = mgh

Law of Conservation of energy states that total energy of the system remains constant.

i.e; Total energy before collision = Total energy after collision

This implies that: the gravitational potential energy lost by m₁ must be equal to sum of gravitational energy gained by m₂ and the elastic potential energy stored in the spring.

$m_1gd = m_2gd+\frac{1}{2}kd^2\\\\m_1g = m_2g+\frac{1}{2}kd\\\\d = \frac{2(m_1-m_2)g}{k}$

d = maximum displacement of the mass m₂