Q230 / 240 · KCET 2026 · Physics
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
- Correct answerD$18$ J
Solution
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
Hence, the correct answer is option: 'D'.