The velocity of a particle executing simple harmonic motion is $16\;cm/s$ at a distance of $8\;cm$ from the mean position and $8\;cm/s$ at a distance of $12\;cm$ from the mean position. Calculate the amplitude of the motion. [Click here for Solution]
[2074 S, 2062, 2050]
A simple pendulum $4\;m$ long swings with an amplitude of $0.2\;m$. Compute the velocity of the pendulum at its lowest point and its acceleration at extreme ends. [Click here for Solution]
[2074 A]
A body of mass $0.1 \; kg$ is undergoing simple harmonic motion of amplitude $1\;m$ and period $0.2\; Second$. If the oscillation is produced by a spring, what will be the maximum value of the force and the force constant of the spring? [Click here for Solution]
[2073 C]
A body of mass $200\;gm$ is executing simple harmonic motion with amplitude of $20\;mm$. The maximum force which acts upon it is $0.8\;N$. Calculate its maximum velocity and its period of oscillation. [Click here for Solution]
[2072 E]
A body of mass 2 kg is suspended from a spring of negligible mass and is found to stretch the spring 0.1 m. What is its force constant and the time period. [Click here for Solution]
[2071 S]
A glider with mass $m = 2 \; kg$ sits on a frictionless horizontal air track, connected to a spring with force constant $k = 5 \; N/m$. You pull the glider, stretching the spring $0.1 \; m$ and then release it with no initial velocity. The glider begins to move back towards ie equilibrium position $(x = 0)$. What is its velocity when $x = 0.08 \; m$? [Click here for Solution]
[2070 C]
A simple pendulum 5m long swings with an amplitude 25 cm. Find the velocity of the pendulum at its lowest point and the acceleration at the end of its path. [Click here for Solution]
[2070 D]
A body is vibrating with simple harmonic motion of amplitude 15 cm and frequency 4 Hz. Calculate the maximum value of acceleration and velocity. [Click here for Solution]
[2069 OLD SET B]
A small mass of 0.2 kg is attached to one end of helical spring and produces an extension of 15 mm. The mass is now set into vertical oscillation of amplitude 10 mm. What is:
(i) The period of oscillation?
(ii) The maximum kinetic energy of the mass?
(iii) The potential of the spring when the mass is 5 mm below the center of oscillation? [Click here for Solution]
[2068 S]
After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 50 cm. She finds that the pendulum makes 100 complete swings in 136 Sec. What is the value of g on this planet? [Click here for Solution]
[2068]
A simple pendulum has a period of 4.2 Second, when the pendulum is shortened by 1 m the period is 3.7 second. From these measurements, calculate the acceleration of free fall and the original length of the pendulum. [Click here for Solution]
[2068 OLD]
A second pendulum is taken tot he moon. If the time period on the surface of the moon is 4.90 seconds, what will bet he acceleration due to gravity of the moon? [Click here for Solution]
[2067]
Calculate the period of oscillation of a simple pendulum of length 1.8 m with a bob of mass 2.2 kg. If the bob of this pendulum is pulled aside a horizontal distance of 20 cm and released. What will be the values of (i) the kinetic energy and (ii) the velocity of the bob at the lowest point of the swing? [Click here for Solution]
[2064]
The displacement y of a mass vibrating with simple harmonic motion is given by $y = 20\; Sin\;10';\pi t$. Where $y$ is in millimeter and $t$ is in second. What is: (i) Amplitude, (ii) The period (iii) The velocity at $t = 0$ [Click here for Solution]
[2060]
A particle of mass 0.3 kg vibrates with a period of 2 seconds. If its amplitude is 0.5 m, what is its maximum kinetic energy? [Click here for Solution]
[2053]
A small mass rests on a horizontal platform which vibrates in simple harmonic motion with a period of 0.25 S. Find the maximum amplitude of the motion which will allow the mass to remain in contact with the platform throughout the motion. [Click here for Solution]
No comments:
Post a Comment