E (Gain) = 17264.55 Q2: The rollercoaster car from Task 1 Q2 above is initially travelling at 6.5m/s at point A in the diagram below. Assuming negligible frictional forces as previously, what will be the final velocity of the car at point B? 6.5m/s 3.5m Initial velocity of the Roller coaster = Vi = 6.5 m/s Final velocity of the Roller Coaster = Vf= ? Mass of Roller Coaster = m = 440Kg Height = h=3.5 Solution Initial Kinetic energy= K.Ei = K.Ei = K.Ei = 9295 Joule Potential energy = P.E = mgh P.E = 440 x 9.8 x 3.5 P.E = 15092 Total Final Energy = P.E + K.Ei Total Final Energy = 9295+15092 Total Final Energy = 24387 joule K.Ef = 24387 joule K.Ef = 24387 = Determine the behaviour of oscillating mechanical systems Q1: Explain simple harmonic motion and relate it to an application of your choice (e.g. an oscillating spring in a suspension system). What conditions are required for resonance and how can this be avoided? (Maximum 500 words) Detailed explanation in appropriate UK technical language, including referenced information sources (not included in word count) required for M. Q2: A stationary diesel generator engine has a stroke of 240mm. The motion of the piston can be assumed to be simple harmonic. a) Calculate the maximum linear velocity and acceleration of the piston at 3000rpm and show at what points in the oscillation they occur Given Data Angular Speed = ?= 3000rpm == 314.16 rad/sec Amplitude = ? R= = 120mm =0.12m Solution V = ? A (at the midpoint) V = 314.16 x 0.12 V = 37.7 m/s (max Piston Velocity at mid point) Next a = ?2 A (At the end of the stroke) a = (314.16)2 x 0.24 a = 11843.58 m/s2 (Acceleration of piston) at the end of the stroke b) Calculate the maximum theoretical force transmitted to the crankshaft bearings if the piston and...
The type of motion is commonly referred to obey the hook’s law, where the force remains directly proportional to the negative acceleration of the mass attached to the spring or pendulum or any other type of simple harmonic motion. The motion is an elastic motion. The mass attached to the spring try to follow a pattern and return to its mean position, when stretched to a particular distance. The mass attached to the spring stores the potential energy when stretched to a particular position and when it is released it releases the kinetic energy. When the mass attached to the spring passes the mean position, it again stores the potential energy and releases the kinetic energy when returning to the mean position. Pendulum shows the similar responses as that of the simple harmonic motion of the mass attached to the spring. The factors that may impact the simple harmonic motion are mass of body attached to the spring, time period, etc.
Resonance is the characteristic of the body or a system to vibrate with more amplitude at particular frequencies more than the other frequencies that are exposed to the system. The frequencies that make the system to vibrate at higher amplitude are often recognized as the resonance frequencies. Most of the systems have particular resonant frequencies. At the resonant mode the system releases the stored energy in the form of loud sound, etc.