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 ..... $\sec$
A$0.13$
B$0.17$
C$0.25$
D$0.33$
Medium
Download our app for free and get started
C$0.25$
c (c) $y = a\sin \frac{{2\pi }}{T}t$
==> $\frac{a}{2} = a\sin \frac{{2\pi t}}{3}$
==> $\frac{1}{2} = \sin \frac{{2\pi t}}{3}$
==> sin$\frac{{2\pi t}}{3} = \sin \frac{\pi }{6}$
==> $\frac{{2\pi t}}{3} = \frac{\pi }{6}$
==> $t = \frac{1}{4}\sec $
Download our app
and get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $M$. The piston and the cylinder have equal cross sectional area $A$. When the piston is in equilibrium, the volume of the gas is $V_0$ and its pressure is $P_ 0$. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency
The metallic bob of simple pendulum has the relative density $5$. The time period of this pendulum is $10\,s$. If the metallic bob is immersed in water, then the new time period becomes $5 \sqrt{ x } s$. The value of $x$ will be.
The bob of a simple pendulum executes simple harmonic motion in water with a period $t$, while the period of oscillation of the bob is ${t_0}$ in air. Neglecting frictional force of water and given that the density of the bob is $(4/3) ×1000 kg/m^3$. What relationship between $t$ and ${t_0}$ is true
In an engine the piston undergoes vertical simple harmonic motion with amplitude $7\, cm$ . A washer rests on top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer no longer stays in contact with the piston, is close to ...... $Hz$
Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is $100 g$. The time period of the motion of the particle will be (approximately) (take $g =10\,ms ^{-2}$, radius of earth $=6400\,km$ )
In the figure given below. a block of mass $M =490\,g$ placed on a frictionless table is connected with two springs having same spring constant $\left( K =2 N m ^{-1}\right)$. If the block is horizontally displaced through ' $X$ 'm then the number of complete oscillations it will make in $14 \pi$ seconds will be $.........$
Aheavy brass sphere is hung from a light spring and is set in vertical small oscillation with a period $T.$ The sphere is now immersed in a non-viscous liquid with a density $1/10\,th$ the density of the sphere. If the system is now set in vertical $S.H.M.,$ its period will be