A 780-g mass is attached to a vertical spring and lowered slowly until the mass

Question

A 780-g mass is attached to a vertical spring and lowered slowly until the mass rests at its equilibrium position 30 cm below the original length of the spring. It is then set into simple harmonic motion of amplitude 5 cm. (a) What is the frequency and period of the oscillation? (b) What is the maximum velocity of the oscillating mass? Where does the maximum velocity occur? (c) What is the maximum acceleration of the oscillating mass? Where does the maximum acceleration occur? (d) Draw a diagram showing how the total energy of the oscillating system changes with time.

Explanation / Answer

the frequency is the number of cycles in a certain time, here it is 5 cycles in 4 seconds and thus the frequency is 1.25 1/s or 1.25 Hz. The Period is the time that the pendulum takes to complete one full cycle. You can divide 4 seconds, the time it takes for 5 cycles by 5 and you get the time for one cycle, 0.8s. You can also use the fact that the period and the frequency are related to each other. The period T and the frequency f must always be reciprocal quantities, meaning that T*f = 1 or 1/f = T and f = 1/T.

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