KCET · Physics · Oscillations
A mass of \(1\) kg is executing SHM. Its displacement is given by \(x = 6.0\cos(100t + \pi/4)\) cm. What is the maximum kinetic energy?
- A \(3\) J
- B \(6\) J
- C \(9\) J
- D \(18\) J
Answer & Solution
Correct Answer
(D) \(18\) J
Step-by-step Solution
Detailed explanation
Given \(m = 1\) kg and \(x = 6.0\cos(100t + \pi/4)\) cm.
Comparing with the standard equation of SHM \(x = A\cos(\omega t + \phi)\), we get:
\(A = 6.0\) cm \(= 0.06\) m
\(\omega = 100\) rad/s
The maximum velocity of the particle is given by \(v_{max} = A\omega\).
\(v_{max} = 0.06 \times 100 = 6\) m/s
The maximum kinetic energy is given by \(K_{max} = \dfrac{1}{2}mv_{max}^2\).
\(K_{max} = \dfrac{1}{2} \times 1 \times (6)^2 = 18\) J
Answer: \(18\) J
Comparing with the standard equation of SHM \(x = A\cos(\omega t + \phi)\), we get:
\(A = 6.0\) cm \(= 0.06\) m
\(\omega = 100\) rad/s
The maximum velocity of the particle is given by \(v_{max} = A\omega\).
\(v_{max} = 0.06 \times 100 = 6\) m/s
The maximum kinetic energy is given by \(K_{max} = \dfrac{1}{2}mv_{max}^2\).
\(K_{max} = \dfrac{1}{2} \times 1 \times (6)^2 = 18\) J
Answer: \(18\) J
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