Question

Problem 4: An object is attached to a spring in such a way that it undergoes simple harmonic motion with a period of 2 s. a) [3 points] What is the angular frequency of the oscillations? b) [3 points] If the mass of the object is 4 kg, what is the value of the spring constant, k? c) [2 points) If the amplitude of the oscillations is 20 cm, what is the total energy of the spring- mass system?

Answer 1

Problem 4 ctiven Period Taas a ) Augular frequency Ex w of oscillations is given by rad/sec w 2TT T g - Wat rad) sec = 3.14 rad) sec w = 3.14 Gad/sec 6) Given mass of object m= 4 kg spring constant k is given by komwa z '. K = 4 *(3:14) N/m k39.44 Nm

c) Given Amplitude 4220 cm 2 20x162 m2 0.2 m, Total Energy of spoing mass system is given by E-KAP E22x39.44*(0.2) ² J anEc0.79 I d) maximum velocity Vmax is given by Umax = AW = 0.8x3:14 mis Umar = 0.628 mis and maximum acceleration aman is given by 0.2 x (3.14)2 m/s² amax = 4 w2 - lamar a 197 m/s2 e) form General formula for SHM when velocity is maximum at too direction is given by is given by and going towards positive act) = Asin(WESI Here & W=3.14 rad /sec. A = 0.2 m so here act) = (0.2 mxsin (3.14 rad xt

A Bonus وه. sin oº - cos cor-90°) sin o= cos co-T1/2) when o is in radian so Here xet) A cos (tot 2) wach act) = Acos (ltro) where & is phase angle & here ø=112 A 20.2 m d w 3.14 rad/sec ..*** act) = (0.2 m) Cos 1. nad 3.14 sext + I rad 2