A body weighing 50 g swings on a thread 25 cm long like a mathematical pendulum.

A body weighing 50 g swings on a thread 25 cm long like a mathematical pendulum. What stiffness does the spring need to take so that when this body is suspended on the spring, it vibrates at the same frequency?

To calculate the required spring stiffness of the resulting spring pendulum, we will use the equality: 1 / 2Π * √ (g / l) = ν (vibration frequency) = 1 / 2Π * √ (k / m), whence g / l = k / m and k = g * m / l.

Variables and constants: g – gravitational acceleration (g ≈ 10 m / s2); m is the mass of the swinging body (m = 50 g = 0.05 kg); l is the length of the thread (l = 25 cm = 0.25 m).

Calculation: k = g * m / l = 10 * 0.05 / 0.25 = 2 N / m.

Answer: You must use a spring with a stiffness of 2 N / m.