Question

a weight of mass 1.60 kg is vibrating vertically on a spring. if the weight moves from its lowest position to its highest position in 0.42 sec, what is the frequency of the weight's oscillation? give your answer in hz to two decimal places. do not include units in your answer.

Answer 1

The weight oscillates with a frequency of 1.19 Hz, calculated by doubling the time of half a cycle (0.42 seconds) to get the full period (0.84 seconds) and then taking the inverse of the period to find the frequency.

Step-by-step explanation:

The frequency of an object in simple harmonic motion like a mass on a spring can be calculated using the time it takes to complete one full cycle (period). Given that this weight takes 0.42 seconds to move from the lowest to the highest position, we need to remember this is half the period since it only represents half of a full oscillation. The full period (T) is therefore 0.42 seconds × 2 = 0.84 seconds. The frequency (f) is the inverse of the period, so we calculate it using the formula f = 1/T.

Therefore, the frequency is:

f = 1/T
f = 1/0.84 s
f = 1.19 Hz

So, the frequency of the weight's oscillation is 1.19 Hz to two decimal places.