If the initial position of a block is x = .16 meters and its initial velocity is - 5 m/s, and K = 100 N/m and M = 3 kg. a) What is the angular frequency w, frequency f, period T? b) What is the amplitude A, phase angle ? c) Write the general equations for x, v, and a. d) What is the absolute value of the maximum values of x, v, a, K.E., U? e) When does the velocity 1st reach its maximum value? f) How many seconds will it take for the PE of spring to equal three times KE of block? (Answers) (Please show general formulas if you can to solve similar problems, thank you) a) w= 5.77 rad/s, f = .92 Hz, T = 1.088 sec b) A = .88 meters, phase angle = 2.96 rads c) x = .88sin(5.77t + 2.96), v = 5.1cos(5.77t + 2.96), a = -29.4sin(5.55t + 2.96) d) xmax= .88 meters, vm= 5.1 m/s, am= 29.4 m/s2, KEm= 38.7 Joules, Um= 38.7 J e) t = .58seconds f)t1= .213sec & t2= .394sec & t3= .758sec & t4= .939sec
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.
If the initial position of a block is x = .16 meters and its initial velocity is - 5 m/s, and K = 100 N/m and M = 3 kg.
a) What is the angular frequency w, frequency f, period T?
b) What is the amplitude A, phase angle ?
c) Write the general equations for x, v, and a.
d) What is the absolute value of the maximum values of x, v, a, K.E., U?
e) When does the velocity 1st reach its maximum value?
f) How many seconds will it take for the PE of spring to equal three times KE of block?
(Answers) (Please show general formulas if you can to solve similar problems, thank you)
a) w= 5.77 rad/s, f = .92 Hz, T = 1.088 sec
b) A = .88 meters, phase angle = 2.96 rads
c) x = .88sin(5.77t + 2.96), v = 5.1cos(5.77t + 2.96),
a = -29.4sin(5.55t + 2.96)
d) xmax= .88 meters, vm= 5.1 m/s, am= 29.4 m/s2, KEm= 38.7 Joules,
Um= 38.7 J
e) t = .58seconds
f)t1= .213sec & t2= .394sec & t3= .758sec & t4= .939sec
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