A spring pendulum weighing m = 0.8 kg oscillates with a period of T = 1.2 s. its total energy

A spring pendulum weighing m = 0.8 kg oscillates with a period of T = 1.2 s. its total energy is E = 2.5 J. find the amplitude of the pendulum’s oscillations. With full design.

Data: m (mass of the used spring pendulum) = 0.8 kg; T (oscillation period) = 1.2 s; E (total energy) = 2.5 J.

Since at the moment V = Vmax the potential energy of the pendulum is equal to zero, and the total will be equal to the kinetic one, then to find the amplitude of oscillations we apply the formula: E = m * Vmax ^ 2/2 = m * (A * ω) ^ 2/2 = m * (A * 2 * Π / T) ^ 2/2, whence A = √ (2E * T ^ 2 / (4 * Π ^ 2 * m) = √ (E * T ^ 2 / (2 * Π ^ 2 * m).

Calculation: A = √ (2.5 * 1.22 / (2 * 3.142 * 0.8) = 0.4777 m.

Answer: The amplitude is 0.4777 m.