MCQ
The periodic time of a body executing simple harmonic motion is $3$ sec. After how much interval from time $t=0$, its displacement will be half of its amplitude
- A$\frac{1}{8} sec$
- B$\frac{1}{6} sec$
- ✓$\frac{1}{4} sec$
- D$\frac{1}{3} sec$
✓
Answer
Correct option: C.
$\frac{1}{4} sec$
$ y=a \sin \frac{2 \pi}{T} t $
$\Rightarrow \frac{a}{2}=a \sin \frac{2 \pi t}{3} $
$\Rightarrow \frac{1}{2}=\sin \frac{2 \pi t}{3} $
$ \Rightarrow \sin \frac{2 \pi t}{3}=\sin \frac{\pi}{6}$
$ \Rightarrow \frac{2 \pi t}{3}=\frac{\pi}{6}$
$\Rightarrow t=\frac{1}{4} \mathrm{sec}$
$\Rightarrow \frac{a}{2}=a \sin \frac{2 \pi t}{3} $
$\Rightarrow \frac{1}{2}=\sin \frac{2 \pi t}{3} $
$ \Rightarrow \sin \frac{2 \pi t}{3}=\sin \frac{\pi}{6}$
$ \Rightarrow \frac{2 \pi t}{3}=\frac{\pi}{6}$
$\Rightarrow t=\frac{1}{4} \mathrm{sec}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The energy of hydrogen atom in its ground state is $-13.6\ eV$. The energy of the level corresponding to the quantum number $n$ is equal $5$ is
→The figures represent three cases of a ray passing through a prism of angle $A$. The case corresponding to minimum deviation is
→Assertion: To convert a galvanometer into an ammeter a small resistance is connected in parallel with it.
Reason: The small resistance increases the combined resistance of the combination.
Pick out the wrong statement
Which is the correct unit for measuring nuclear radii
The relationship between force and position is shown in the figure given (in one dimensional case). The work done by the force in displacing a body from $x=1 \mathrm{~cm}$ to $x=5 \mathrm{~cm}$ is
→A micro-wave and an ultrasonic sound wave have the same wavelength. Their frequencies are in the ratio (approximately)
A small steel ball of radius $r$ is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $\eta$.After some time the velocity of the ball attains a constant value known as terminal velocity $v_T$. The terminal velocity depends on (i) the mass of the ball $m$, (ii) $\eta$, (iii) $r$ and (iv) acceleration due to gravity $g$. Which of the following relations is dimensionally correct
→Television signals broadcast from the moon can be received on the earth while the TV broadcast from Delhi cannot be received at places about $100 km$ distant from Delhi. This is because
→A copper wire has a square cross-section, $2.0 \mathrm{~mm}$ on a side. It carries a current of $8 A$ and the density of free electrons is $8 \times 10^{28} \mathrm{~m}^{-3}$. The drift speed of electrons is equal to
→