How many times will the oscillation period of a spring pendulum change if its mass is reduced by 2 times, and the stiffness of the spring is increased by 2 times.
The period of oscillation of the spring pendulum before changes:
T = 2π√ (m / k), where m is the mass of the load, k is the stiffness of the spring.
Weight and spring stiffness after changes:
m1 = m / 2;
k1 = 2k.
T1 = 2π√ (m1 / k1) = 2π√ ((m / 2) / (2k)) = 2π√ (m / (4k)) = π√m / k.
T / T1 = (2π√ (m / k)) / (π√ (m / k)) = 2.
T1 = T / 2.
Answer. The oscillation period of the pendulum will be halved.
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