A force of $6.4\ N$ stretches a vertical spring by $0.1\ m$. The mass that must be suspended from the spring so that it oscillates with a time period of $\pi/4\ second$ is .... $kg$
Medium
Download our app for free and get started
Spring constant $\mathrm{K}=\frac{6.4}{0.1}=64 \mathrm{N} / \mathrm{m}$
Now $\quad \mathrm{T}=2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$
or $\frac{\pi}{4}=2 \pi \sqrt{\frac{\mathrm{m}}{64}}$
$\therefore m=1 \mathrm{kg}$
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
- 1When the potential energy of a particle executing simple harmonic motion is one-fourth of its maximum value during the oscillation, the displacement of the particle from the equilibrium position in terms of its amplitude $a$ isView Solution
- 2The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is $10\,s^{-1}$. At, $t = 0$ the displacement is $5\, m$. What is the maximum acceleration ? The initial phase is $\frac{\pi }{4}$View Solution
- 3The displacement of an object attached to a spring and executing simple harmonic motion is given by $ x= 2 \times 10^{-9}$ $ cos$ $\;\pi t\left( m \right)$ .The time at which the maximum speed first occurs isView Solution
- 4The kinetic energy of a particle executing $S.H.M.$ is $16\, J$ when it is at its mean position. If the mass of the particle is $0.32 \,kg$, then what is the maximum velocity of the particle ..... $m/s$View Solution
- 5Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated in the figure. The simple harmonic motion of the $x-$ projection of the radius vector of the rotating particle $P$ isView Solution
- 6Two particles $P$ and $Q$ describe simple harmonic motions of same period, same amplitude, along the same line about the same equilibrium position $O.$ When $P$ and $Q$ are on opposite sides of $O$ at the same distance from $O$ they have the same speed of $1.2 \,m/s$ in the same direction, when their displacements are the same they have the same speed of $1.6\, m/s$ in opposite directions. The maximum velocity in $m/s$ of either particle isView Solution
- 7In forced oscillation of a particle the amplitude is maximum for a frequency $\omega_{1}$ of the force, while the energy is maximum for a frequency $\omega_{2}$ of the force, thenView Solution
- 8The time period of a second's pendulum is $2\, sec$. The spherical bob which is empty from inside has a mass of $50\, gm$. This is now replaced by another solid bob of same radius but having different mass of $ 100\, gm$. The new time period will be .... $\sec$View Solution
- 9A particle executes simple harmonic motion with a frequency $f$. The frequency with which its kinetic energy oscillates isView Solution
- 10If displacement $x$ and velocity $v$ are related as $4v^2 = 25 -x^2$ in a $SHM$. Then time Period of given $SHM$ is (Consider $SI\, units$)View Solution