The load vibrates in a vertical plane on a rubber cord. How many times will the oscillation period

The load vibrates in a vertical plane on a rubber cord. How many times will the oscillation period change if the load is suspended on the same cord folded in half?

k2 = 2 * k1.
T1 / T2 -?
The period of the spring pendulum T is determined by the formula: T = 2 * P * √ (m / k), where P is the number pi, m is the mass of the load that is suspended from the pendulum, k is the rigidity of the rubber cord.
When the rubber cord is folded in half, the rigidity is doubled: k2 = 2 * k1.
T1 = 2 * P * √ (m / k1).
T2 = 2 * P * √ (m / k2) = 2 * P * √ (m / 2 * k1).
T1 / T2 = 2 * P * √ (m / k1) / 2 * P * √ (m / 2 * k1) = √2 = 1.4.
Answer: the period of oscillation of the spring pendulum will decrease by 1.4 times: T1 / T2 = 1.4.



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