A $1 \,kg$ block attached to a spring vibrates with a frequency of $1\, Hz$ on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an $8\, kg$ block placed on the same table. So, the frequency of vibration of the $8\, kg$ block is ..... $Hz$
JEE MAIN 2017, Medium
Download our app for free and get started
Frequency of spring $(f)=\frac{1}{2 \pi} \sqrt{\frac{k}{m}}=1 \mathrm{Hz}$
$\Rightarrow 4 \pi^{2}=\frac{\mathrm{k}}{\mathrm{m}}$
If block of mass $\mathrm{m}=1 \mathrm{kg}$ is attached then, $k=4 \pi^{2}$
Now, identical springs are attached in parallel with mass
$\mathrm{m}=8 \mathrm{kg}$, Hence, $k_{e q}=2 k$
$f^{\prime}=\frac{1}{2 \pi} \sqrt{\frac{\mathrm{k} \times 2}{8}}=\frac{1}{2} \mathrm{Hz}$
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 particle is vibrating in a simple harmonic motion with an amplitude of $4\, cm.$ At what displacement from the equilibrium position, is its energy half potential and half kineticView Solution
- 2The resultant of two rectangular simple harmonic motions of the same frequency and unequal amplitudes but differing in phase by $\frac{\pi }{2}$ isView Solution
- 3Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass $=500\, g$, Decay constant $=20 \,g / s$ then ...... $s$ time is required for the amplitude of the system to drop to half of its initial value ? $(\ln 2=0.693)$View Solution
- 4$Assertion :$ In simple harmonic motion, the velocity is maximum when the acceleration is minimum.View Solution
$Reason :$ Displacement and velocity of $S.H.M.$ differ in phase by $\frac{\pi }{2}$ - 5A block of mass $m$ rests on a platform. The platform is given up and down $SHM$ with an amplitude $d$ . What can be the maximum frequency so that the block never leaves the platformView Solution
- 6The 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.View Solution
- 7The function $(sin\,\omega t -cos\,\omega t)$ representsView Solution
- 8View SolutionThe mass and diameter of a planet are twice those of earth. The period of oscillation of pendulum on this planet will be (If it is a second's pendulum on earth)
- 9Amplitude of a wave is represented by $A = \frac{c}{{a + b - c}}$ Then resonance will occur whenView Solution
- 10If $x, v$ and $a$ denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period $T$, then, which of the following does not change with time?View Solution