Spring constant of the spring, amplitude of the motion, and frequency of oscillation are respectively 8N/m, 1.2 cm and 2Hz.
To find the answer, we need to know about angular frequency, frequency, amplitude of spring mass system.
What's the angular frequency of the spring mass system, if its time period is 0.5 second?
- Mathematically, w=2π/T
- w= 2π/0.5= 12.6 rad/s
What's the relation between angular frequency and spring constant?
- Mathematically, w =√(k/m)
- k= w²m
- Here, w= 12.6 rad/s, m= 50gm = 0.05kg
- k= 12.6²× 0.05 = 8 N/m
What's the relation between amplitude, angular frequency and velocity of mass of a spring mass system?
- Mathematically, Amplitude= velocity/angular frequency
- Here, velocity= 15 cm/s = 0.15m/s, angular frequency= 12.6 rad/s
- Amplitude= 0.15/12.6= 0.012m = 1.2 cm
What's the expression of frequency in term of time period?
- Frequency= 1/time period
- Here time period= 0.5 s
- Frequency= 1/0.5 = 2 Hz
Thus, we can conclude that spring constant of the spring, amplitude of the motion, and frequency of oscillation are respectively 8N/m, 1.2 cm and 2Hz.
Learn more about the spring mass system here:
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