The time period T of the object is 2.09 seconds
Given
Mass of the object = m (considered as a variable).
The amplitude of the object = 12 cm.
Acceleration of the object = 108 cm2/s.
We have to find the Time period of the object= T (let’s assume)
We know from Harmonics
Acceleration of the object = (Amplitude of the object) * (Frequency of the object)2
⇒ 108 cm2/s = 12 cm * (ω)2
⇒ 108/12 = (ω)2
⇒ 9 = (ω)2
⇒ 3 = (ω)
Therefore, the frequency of the object = 3 Hz
Also
We know that
Frequency of the object = (2π) / (Time-Period of the object)
⇒ 3 Hz= (2π) / (Time-Period of the object)
⇒ Time-Period of the object = (2π)/3
⇒ T= 2.09 seconds
Hence Time Period of the object = 2.09 seconds
Learn more about time-period of simple harmonic motion
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