First slide

Applications of SHM

Question

A man weighing 60 kg stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude 0.1 m and frequency $\frac{2}{π} Hz$ . Which of the following statement is correct?

Moderate

A

The spring balance reads the weight of man as 60 kg
B

The spring balance reading fluctuates between 60 kg. and 70 kg
C

The spring balance reading fluctuates between 50 kg and 60 kg
D

The spring balance reading fluctuates between 50 kg and 70 kg

Solution

The maximum force acting on the body executing simple harmonic motion is
$m ω^{2} a = m \times (2 π f)^{2} a = 60 \times {(2 π \times \frac{2}{π})}^{2} \times 0.1 N$
$= 60 \times 16 \times 0.1 = 96 N = \frac{96}{9.8} \approx 10 kgf$ and this force is towards mean position.
The reaction of the force on the platform away from the mean position. It reduces the weight of man on upper extreme i.e. net weight = (60 - 10) kgf.
This force adds to the weight at lower extreme position i.e. net weight becomes = (60 + 10) kgf.
Therefore, the reading the weight recorded by spring balance fluctuates between 50 kgf and 70 kgf.

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