A body attached to a spring undergoes SHM of frequency 5 Hz along x-axes. If the displacement from equilibrium is x = 4 cm, find the acceleration.
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
1) A body attached to a spring undergoes SHM of frequency 5 Hz along x-axes. If the displacement from equilibrium is x = 4 cm, find the acceleration.
2) A mass atttached to a spring vibrates with SHM of frequency 5 Hz and amplitude 5 cm.What is the maximum speed that the mass can attain?
4) A particle undergoes SHM according to the law x= - (5 cm)cos[(4 s -1 )t + π]. Find the amplitude, angular frequency and initial phase of oscillations.
5) The position of a mass oscillating on a spring is given by x = (3.2 m) cos[2πt/(0.58 s)]. (a) What is the period of this motion? (b) What is the first time the mass is at the position x = 0?
6) A mass m = 8.0 kg is attached to a spring and allowed to hang in the Earth's gravitational field. The spring stretches 3.6 cm before it reaches its equilibrium position. If allowed to oscillate, what would be its frequency?
7) A 4.8 kg block attached to a spring executes
8) A 0.16 kg block on a horizontal frictionless surface is attached to a spring whose force constant is 360 N/m. The block is pulled from its equilibrium position at x = 0 m to a displacement x = 0.080 m and is released from rest. The block then executes simple harmonic motion along the x-axis (horizontal). When the displacement is x = 0.037 m, what is the acceleration of the block?
9) A mass oscillates with SHM along x-axis with period T and initial phase α = 0. What is the angle between x-axis and the phasor representing the velocity of the mass at time t = 0,7 T?
10) A particle is subjected to two SHM of the same direction and angular frequency ω. The two SHM have amplitudes A and 2A and initial phases 0° and 120°, respectively. Find the equation of the resultant oscillation.
11) A 0.39 kg block on a horizontal frictionless surface is attached to a spring whose force constant is 570 N/m. The block is pulled from its equilibrium position at x = 0 m to a displacement x = 0.080 m and is released from rest. The block then executes simple harmonic motion along the x-axis (horizontal). If the displacement is x = 0.057 m, find the kinetic energy of the block.
12) A 2-kg mass attached to a spring oscillates in simple harmonic motion and has a speed of 5 m/s at the equilibrium point. What is the maximum potential energy of this oscillating mass?
13) If the amplitude of damped oscillations has been reduced 4 times, how many times the maximum value of the restoring force is decreased?
14) An underdamped spring-mass system consists of a spring with a force constant of 2.00 N/m and a mass of 550 g. It is observed that the oscillations decrease in magnitude by 10.0% every 360 s. What is the value of the damping constant for the system?
15) A 1200-kg car whose springs have an effective force constant of 2.66×106 N/m is moving along the highway with its tires out of balance. The tires have a radius of 40.6 cm. At what speed will the driver experience large vibrations?
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
