A body executes sample harmonic motion under the action of a force $F_1$ with a time period $(4 / 5)\ sec$. If the force is changed to $F_ 2$ it executes $SHM$ with time period $(3 / 5)\ sec$. If both the forces $F_1$ and $F_2$ act simultaneously in the same direction on the body, it's time period (in $second$) is
Diffcult
Download our app for free and get started
$F_{1}=m \omega^{2} x$
$T=\frac{2 \pi}{\omega}$
$F=m a=4 m \pi^{2} x \frac{1}{T^{2}}$
$\therefore F_{1}=\frac{4 m \pi^{2}}{T_{1}^{2}} x$
$F_{2}=\frac{4 m \pi^{2}}{T_{2}^{2}} x$
$F_{1}+F_{2}=\frac{4 m \pi^{2} x}{T^{2}}+\frac{4 m \pi^{2} x}{T_{2}^{2}}$
$\frac{1}{T^{2}}=\frac{1}{T_{1}^{2}}+\frac{1}{T_{2}^{2}}$
$\therefore T=\frac{12}{25}$
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
- 1A body is executing simple harmonic motion with an angular frequency $2\,rad/s$. The velocity of the body at $20\, mm$ displacement, when the amplitude of motion is $60\, mm$, is ...... $mm/s$View Solution
- 2A particle is executing $S.H.M.$ and its velocity $v$ is related to its position $(x)$ as $v^2+a x^2=b$, where $a$ and $b$ are positive constants. The frequency of oscillation of particle is ..........View Solution
- 3The velocity vector $v$ and displacement vector $x$ of a particle executing SHM are related as $\frac{v d v}{d x}=-\omega^2 x$ with the initial condition $v=v_0$ at $x=0$. The velocity $v$, when displacement is $x$, isView Solution
- 4The energy of a particle executing simple harmonic motion is given by $E = Ax^2 + Bv^2$, where $x$ is the displacement from mean position $x = 0$ and $v$ is the velocity of the particle at $x$ then choose the incorrect statementView Solution
- 5Which of the following expressions corresponds to simple harmonic motion along a straight line, where $x$ is the displacement and $a, b, c$ are positive constants?View Solution
- 6Two particle executing $S.H.M.$ of same amplitude of $20 \,cm$ with same period along the same line about same equilibrium position. The maximum distance between the two is $20 \,cm$. Their phase difference in radian is equal toView Solution
- 7The velocity-time diagram of a harmonic oscillator is shown in the adjoining figure. The frequency of oscillation is ..... $Hz$View Solution
- 8View SolutionWhich of the following statements is not true ? In the case of a simple pendulum for small amplitudes the period of oscillation is
- 9Two pendulums of length $121\,cm$ and $100\,cm$ start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean position is :View Solution
- 10Two damped spring-mass oscillating systems have identical spring constants and decay times. However, system $A's$ mass $m_A$ is twice system $B's$ mass $m_B$ . How do their damping constants, $b$ , compare ?View Solution