1
KCET 2023
+1
-0

A block of mass $$m$$ is connected to a light spring of force constant $$k$$. The system is placed inside a damping medium of damping constant $$b$$. The instantaneous values of displacement, acceleration and energy of the block are $$x, a$$ and $$E$$ respectively. The initial amplitude of oscillation is $$A$$ and $$\omega^{\prime}$$ is the angular frequency of oscillations. The incorrect expression related to the damped oscillations is

A
$$x=A e^{-\frac{b}{m}} \cos \left(\omega^{\prime} t+\phi\right)$$
B
$$\omega^{\prime}=\sqrt{\frac{k}{m}-\frac{b^2}{4 m^2}}$$
C
$$E=\frac{1}{2} k A^2 e^{-\frac{b t}{m}}$$
D
$$m \frac{d^2 x}{d t^2}+b \frac{d x}{d t}+k x=0$$
2
KCET 2022
+1
-0

The displacement of a particle executing SHM is given by $$x=3 \sin \left[2 \pi t+\frac{\pi}{4}\right]$$, where $$x$$ is in metre and $$t$$ is in seconds. The amplitude and maximum speed of the particles is

A
$$3 \mathrm{~m}, 4 \pi \mathrm{ms}^{-1}$$
B
$$3 \mathrm{~m}, 6 \pi \mathrm{ms}^{-1}$$
C
$$3 \mathrm{~m}, 8 \pi \mathrm{ms}^{-1}$$
D
$$3 \mathrm{~m}, 2 \pi \mathrm{ms}^{-1}$$
3
KCET 2021
+1
-0

A pendulum oscillates simple harmonically and only if

I. the sizer of the bob of pendulum is negligible in comparison with the length of the pendulum.

II. the angular amplitude is less than $$10^{\circ}$$.

Choose the correct option.

A
Both I and II
B
Only I
C
Only II
D
None of these
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