First slide

Simple harmonic motion

Question

A body of mass 1kg executing S.H.M., its displacement y cm at t seconds is given by $y = 6 \sin π (\frac{100}{π} t + \frac{1}{4})$ . Its maximum kinetic energy is

Moderate

A

6J
B

18J
C

24J
D

36J

Solution

For a body executing simple harmonic motion the maximum kinetic energy will be at its mean position. We know that,
Mechanical energy = Potential Energy + Kinetic energy
At mean position potential energy is 0. Hence the mechanical energy will be equal to maximum kinetic energy.
Mechanical energy = $\frac{1}{2} m ω^{2} A^{2}$
Where m=1kg, $ω = 100 r a d / s$ , A=0.06m
Substituting this in the relation for maximum kinetic energy i.e. mechanical energy, we get
ME = $\frac{1}{2} (1 \times 100^{2} \times {0.06}^{2})$
Hence ME = $\frac{1}{2} (36) = 18 J$ .

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