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A mass m is vertically suspended from a spring of negligible mass. The system oscillates with a frequency n. What will be the frequency of the system, if a mass 4m is suspended from the same spring ?
- a)n/4
- b)4n
- c)n/2
- d)2n
Correct answer is option 'C'. Can you explain this answer?
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A mass m is vertically suspended from a spring of negligible mass. The...
Given, a mass m is vertically suspended from a spring of negligible mass and the system oscillates with a frequency n.
Frequency of the system:
The frequency of the system is given by the formula:
f = 1/2π √(k/m)
where k is the spring constant and m is the mass of the object.
Frequency of the system with mass 4m:
Now, if a mass 4m is suspended from the same spring, the frequency of the system can be calculated using the same formula:
f' = 1/2π √(k/4m)
Since k is constant for the same spring, we can simplify the above equation as:
f' = 1/2π √(1/4) √(k/m)
f' = 1/2π (1/2) √(k/m)
f' = 1/4π √(k/m)
Comparing the above equation with the frequency of the system, we can see that:
f' = f/2
Therefore, the frequency of the system when a mass 4m is suspended from the same spring is half the frequency of the system when a mass m is suspended from the spring.
Hence, the correct option is (c) n/2.
Frequency of the system:
The frequency of the system is given by the formula:
f = 1/2π √(k/m)
where k is the spring constant and m is the mass of the object.
Frequency of the system with mass 4m:
Now, if a mass 4m is suspended from the same spring, the frequency of the system can be calculated using the same formula:
f' = 1/2π √(k/4m)
Since k is constant for the same spring, we can simplify the above equation as:
f' = 1/2π √(1/4) √(k/m)
f' = 1/2π (1/2) √(k/m)
f' = 1/4π √(k/m)
Comparing the above equation with the frequency of the system, we can see that:
f' = f/2
Therefore, the frequency of the system when a mass 4m is suspended from the same spring is half the frequency of the system when a mass m is suspended from the spring.
Hence, the correct option is (c) n/2.
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A mass m is vertically suspended from a spring of negligible mass. The system oscillates with a frequency n. What will be the frequency of the system, if a mass 4m is suspended from the same spring ?a)n/4b)4nc)n/2d)2nCorrect answer is option 'C'. Can you explain this answer?
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