Question 2: An object with a mass
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Can you solve it plz
An object with a mass of 0.5kg and potential energy
expressed as the image
equlibrium point x=0. What is the
angular frequency of this object?
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Solved in 4 steps
- Consider a mass m attached to a spring with natural length 7, hanging vertically under the action of gravity mgk (where the unit vector k is pointing downwards) and a constant friction force F =-Fok. (a) Find the equilibrium point of the mass, write the equation of motion, and show that the motion of the particle is governed by the fundamental equation of simple harmonic motion. (b) Assume the particle is released from the spring when it has heighth above ground and initial velocity vo. Let y be the height above ground of the particle (note that the orientation of the axis is now opposite of z used in point (a)). Write the equation of motion (under the action of gravity and the friction force F). Solve them for the given initial condition and show that v(y)² = vz+2(g− ¹)(h—−y) m (c) Upon entering the ground (y=0) with velocity v₁, the particle is subject to a constant friction force F₁ where F₁ >0 is a constant. Calculate the distance d travelled by the particle into the ground in…and a damping Constand= 15 with 8-Kg mass 0.5 meters beyond If spring its natural length by a can be Styefzhed 1.5 newtons - Suppo sod natural length and then releasetd wim zero velocit y force of the sering is slredched 1 meter beyond irs ン I obta in c and How could (2 equationsA particle vibrated at a frequency of 100 hz and a amplitude of 0.03 cm Calculate speed and particle acceleration at Max junction. Specify the position of particles as a function of time!
- Consider a which m" ů O•os hq and 'k is 5ONm. State and sketch the nature f oscillatog. motion when the damping Constant b is )0.1N - s/m li) L-ON-5/m and SN-5/m. damped hamardk osallator derWhy is it only possible to produce the odd harmonics in a system with oneopen end and one closed end.A mass on a spring is held at a distance of 0.05 m from the equalibrium position. It is then released at time t=0 and undergoes simple harmonic motion. If the mass was 0.2 kg and the spring constant k was 6 Nm-1, what is the velocity of the mass at time = 7 seconds?
- thin re is measured The second harmonic frequency for a long at 200 Hz when it is attached to the ceiling with amass in tied to its bottom. Adding an extra lkg to the hanging mass increases the second harmonic Frequency to 245 M₂. Findm [draw appropriate diagrams to explain]What is the max speed and the max acceleration of this figure and these values.