A particle with a mass of is oscillating with simple harmonic motion with a period of and a maximum speed of .
We can find the angular frequency by using the time period of motion. And maximum displacement can be found by using the formulae of maximum velocity and angular frequency.
Angular frequency of a body in oscillation
The velocity of a body undergoing simple harmonic motion
Using equation (i) and the given values, the angular frequency is given as follows:
Hence, the angular frequency is .
Using the given values and equation (ii), we get the maximum displacement as follows:
Hence, the maximum displacement is .
A 3.0kg particle is in simple harmonic motion in one dimension and moves according to the equation x=(5.0 m)cos ,with t in seconds. (a) At what value of x is the potential energy of the particle equal to half the total energy? (b) How long does the particle take to move to this position x from the equilibrium position?
A massless spring hangs from the ceiling with a small object attached to its lower end. The object is initially held at rest in a position such that the spring is at its rest length. The object is then released from and oscillates up and down, with its lowest position being
(a) What is the frequency of the oscillation?
(b) What is the speed of the object when it is below the initial position?
(c) An object of mass is attached to the first object, after which the system oscillates with half the original frequency. What is the mass of the first object?
(d) How far below is the new equilibrium (rest) position with both objects attached to the spring?
A 2.0 kg block is attached to the end of a spring with a spring constant of 350 N/m and forced to oscillate by an applied force , where . The damping constant is , the block is at rest with the spring at its rest length. (a) Use numerical integration to plot the displacement of the block for the first 1.0 s. Use the motion near the end of the 1.0 s interval to estimate the amplitude, period, and angular frequency. Repeat the calculation for (b) and (c) .
A block sliding on a horizontal frictionless surface is attached to a horizontal spring with a spring constant of . The block executes SHM about its equilibrium position with a period of and an amplitude of . As the block slides through its equilibrium position, a role="math" localid="1657256547962" putty wad is dropped vertically onto the block. If the putty wad sticks to the block, determine (a) the new period of the motion and (b) the new amplitude of the motion.
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