Determine the number of full vibrations that a 4 kg load suspended on a spring with a stiffness of 400 N / m will make during 30 s.

m = 4 kg.

k = 400 N / m.

t = 30 s.

N -?

To find the number of full oscillations of a spring pendulum N, it is necessary to divide the oscillation time t by the time of one full oscillation T, which is called the oscillation period: N = t / T.

For a spring pendulum, the period of natural free oscillations T is determined by the formula: T = 2 * п * √m / √k, where P is the number pi, m is the mass of the load, k is the stiffness of the spring.

N = t * √k / 2 * п * √m.

N = 30 s * √400 N / m / 2 * 3.14 * √4 kg = 47.7 = 47.

Answer: the pendulum will make N = 47 complete oscillations.