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4.100 Maximum acceleration in simple harmonic motion

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...

4.99 Maximum speed in simple harmonic motion

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...

4.98 Length of a pendulum

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...

4.97 Time period of oscillation

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...

4.96 Amplitude of oscillation of a spring

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...

4.95 Compression and rarefaction in a longitudinal wave

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...

4.94 Amplitude of oscillation

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?...

4.93 Total energy of a particle in SHM

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...

4.92 Change in momentum in simple harmonic motion

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...

4.91 Amplitude of oscillation of a spring block system

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...

4.90 Time period of a simple pendulum in accelerated lift

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...