A particle of mass $250\,g$ executes a simple harmonic motion under a periodic force $F =(-25\,x) N$. The particle attains a maximum speed of $4\,m / s$ during its oscillation. The amplitude of the motion is $...........cm$.
JEE MAIN 2023, Medium
Download our app for free and get started
$\frac{1}{4} a =-25 x \quad ; \quad a =-100 x$
$\omega^2=100 \quad \omega=10$
$\omega A =4$ $\quad A=\frac{4}{10}=0.4\,m$
$A =40\,cm$
Download our appand 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.*
Similar Questions
- 1View SolutionTwo particles are oscillating along two close parallel straight lines side by side, with the same frequency and amplitudes. They pass each other, moving in opposite directions when their displacement is half of the amplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is
- 2A particle executes simple harmonic motion represented by displacement function as $x(t)=A \sin (\omega t+\phi)$View Solution
If the position and velocity of the particle at $t=0\, {s}$ are $2\, {cm}$ and $2\, \omega \,{cm} \,{s}^{-1}$ respectively, then its amplitude is $x \sqrt{2} \,{cm}$ where the value of $x$ is ..... .
- 3A rod of mass $m$ and length $l$ is suspended from ceiling with two string of length $l$ as shown. When the rod is given a small push in the plane of page and released time period is $T_1$ and when the rod is given a push perpendicular to plane time period of oscillation is $T_2$ . The ratio $\frac{{T_1^2}}{{T_2^2}}$ isView Solution
- 4Two particles are executing $SHM$ of the same amplitude $A$ and frequency $\omega $ along the $x-$ axis. Their mean position is separated by $X_0$ (where $X_0 > A$ ). If maximum separation between them is $X_0 + 2A$ , then the phase difference between their motion isView Solution
- 5Three mass and string system is in equilibrium. When $700\,gm$ mass is removed, then the system oscillates with a period of $3\,seconds$ . When the $500\,gm$ mass is also removed, then what will be new time period for system ..... $\sec$View Solution
- 6A uniform stick of mass $M$ and length $L$ is pivoted at its centre. Its ends are tied to two springs each of force constant $K$ . In the position shown in figure, the strings are in their natural length. When the stick is displaced through a small angle $\theta $ and released. The stickView Solution
- 7The ratio of frequencies of two pendulums are $2 : 3$, then their length are in ratioView Solution
- 8$m x^{2}-b x+k=0$View Solution
Find time after which to the energy will become half of initial maximum value in damped force oscillation.
- 9For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is $1\,kg$, the angular frequency is $\omega_1$. When the mass block is $2\,kg$ the angular frequency is $\omega_2$. The ratio $\omega_2 / \omega_1$ isView Solution
- 10View SolutionThe diagram shows two oscillations. What is the phase difference between the oscillations?
