by Rajan M V | Jan 16, 2015 | Oscillations and waves

4.100: A mass of $4\: kg$ suspended from a spring of force constant $800 \:Nm^{-1}$ executes simple harmonic oscillations. If the total energy of the oscillator is $4\:J$, determine the maximum acceleration in $ ms^{-2}$ of the mass. Solution: Angular frequency of...
by Rajan M V | Jan 15, 2015 | Oscillations and waves

A spring of force constant $1200 \:N m^{-1}$ is mounted on a horizontal table as shown in figure. A mass of $3 \:kg$ is attached to its free end and pulled sideways to a distance of $2\: cm$ and released. Calculate the maximum velocity of the mass. Solution: When...
by Rajan M V | Jan 14, 2015 | Oscillations and waves

Problem 4.98: A simple pendulum is released at rest while its string is making an angle of $10^o$ with the vertical. $0.2$ seconds later the string makes an angle of $5^o$ with the vertical. Determine the length of the pendulum. Take acceleration due to gravity as...
by Rajan M V | Jan 13, 2015 | Oscillations and waves

Problem 4.97: A block of mass $M$ kept on a smooth horizontal surface is connected to three identical springs each with constant $k$. Determine the time period for small amplitude oscillations. Neglect all dissipating forces. Solution: When the block is displaced to...
by Rajan M V | Jan 12, 2015 | Oscillations and waves

Problem 4.96: A block of mass $M$ is connected to a series connection of two springs with spring constants $k_1$ and $k_2$ respectively. This is shown in the diagram. If the block oscillates in a simple harmonic fashion with amplitude determine the amplitude of...
by Rajan M V | Jan 11, 2015 | Oscillations and waves

Problem 4.95: In a longitudinal wave there is state of maximum compression at a point at an instant. The frequency of wave is 50 Hz. After what time will the same point be in the state of maximum rarefaction. Solution: When a longitudinal wave propagates through a...
by Rajan M V | Jan 11, 2015 | Oscillations and waves

Problem 4.94: A block of mass $M$ on a smooth horizontal surface is connected to a mass less spring of length $L$ and spring constant $k$. The block is displaced by a distance $A$ and released. What is the amplitude of oscillation of the midpoint $P$ of the spring?...
by Rajan M V | Jan 9, 2015 | Oscillations and waves

Problem 4.93: A block of mass $0.2\:kg$ is attached to a vertical spring of constant $100\:Nm^{-1}$. When the block is at rest it is at a height of $2\:m$ from the ground below. At time $t\:=\:0$ the particle starts simple harmonic motion given by the equation...
by Rajan M V | Jan 8, 2015 | Oscillations and waves

Problem 4.92: A block of mass $M$ connected to a spring of constant $K$ is resting on a smooth horizontal surface ass shown. The block is pulled from this position through a distance $X$ and then released. Determine the change in momentum as the block crosses the...
by Rajan M V | Jan 7, 2015 | Oscillations and waves

Problem 4.91: A block of mass $M$ connected to a mass-less spring of constant is placed on a smooth horizontal surface as shown. A particle of mass $M$ is projected from a block with a speed of $10\:ms^{-1}$ at an angle of $60^o$. Determine the amplitude of the...
by Rajan M V | Jan 5, 2015 | Oscillations and waves

Problem 4.90: A simple pendulum consisting of an inextensible string of length $L$ and mass $m$ is oscillating in a stationary lift with a period of $2$ second. The lift then accelerates upwards with a constant acceleration of $5\:ms^{-2}$. What will be the time...
by Rajan M V | Jan 4, 2015 | Oscillations and waves

Problem 4.89: The displacement of a particle varies according to the relation $x\: =\: 4 (cos \pi t + sin \pi t)$. Determine the amplitude of the motion of the particle. Solution: The equation represents the sum of two simple harmonic motions. One of it is $x\: =\: 4...
by Rajan M V | Jan 1, 2015 | Oscillations and waves

Problem 4.88: A block of mass $15\: kg$ executes SHM under the restoring force of a spring. The amplitude and the time period of the motion are $0.1 \:m$ and $3.14 \:s$ respectively. Find the maximum force exerted by the spring on the block. Solution: In simple...
by Rajan M V | Dec 31, 2014 | Oscillations and waves

Problem 4.87: What is the length of a simple pendulum, which ticks seconds ? Take acceleration due to gravity as $9.8\:ms^{-2}$. Solution: Time period of a simple pendulum with length $L$ is given by, $T\:=\:2\pi \sqrt{\frac{L}{g}}$. When a pendulum ticks second, each...
by Rajan M V | Dec 22, 2014 | Oscillations and waves

Problem 4.87: Two sound waves having wavelength of $50\:cm$ and $51\:cm$ produces $12$ beats per second. Determine the speed sound in the medium. Solution: Wavelength $\lambda$, frequency $\nu$ and speed $v$ of a wave are related as $v\:=\:\nu\:\lambda$. So frequency...
by Rajan M V | Dec 21, 2014 | Featured, Oscillations and waves

Problem 4.86: A block of mass $M\:kg$ is attached to a mass-less spring of force constant $K$ on a smooth surface as shown in the diagram. A particle of mass $M\:kg$ is projected from the block with a speed of $10\:ms^{_1}$ at an angle of $60^0$ with the horizontal....
by Rajan M V | Dec 20, 2014 | Oscillations and waves

Problem 4.85: A particle of mass $M$ is in simple harmonic motion of amplitude $A$ and time period $T$ along a straight line. Determine the change in momentum when the particle goes from the mean position to one of the extremes. Solution: In the case of simple...
by Rajan M V | Dec 19, 2014 | Oscillations and waves

Problem 4.84: A $100 \:cm$ long wire of mass $40\:g$ supports a block of mass of $1.6 \:kg$ as shown. Find the fundamental frequency of the portion of the string between the wall and the pulley. Take $g \:=\: 10\:ms^{-1}$. Solution: Fundamental frequency of a...