# 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. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.