A 50g mass is vibrating in SHM with an amplitude of 12 cm and a period of 1.70 s. The frequency of the oscillation is:
Understand the Problem
The question is asking us to calculate the frequency of oscillation given the period of the SHM. We know frequency is the inverse of the time period, therefore it can be calculated using (f = 1/T)
Answer
$f = 0.5 \text{ Hz}$
Answer for screen readers
$f = 0.5 \text{ Hz}$
Steps to Solve
- Identify the given value
The problem states that the period, $T$, is 2.0 seconds
- Apply the formula relating frequency and period
The frequency, $f$, is the inverse of the period, $T$. Therefore: $$ f = \frac{1}{T} $$
- Substitute the given period into the formula
Substitute $T = 2.0$ seconds into the formula:
$$ f = \frac{1}{2.0} $$
- Calculate the frequency
$$ f = 0.5 \text{ Hz} $$
$f = 0.5 \text{ Hz}$
More Information
The unit of frequency is Hertz (Hz), which is equivalent to cycles per second.
Tips
A common mistake is to confuse the period and the frequency. Remembering that they are inversely related (i.e., $f = 1/T$) helps avoid this confusion. Another mistake is using the incorrect units or not including the units in the final answer.
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