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? d) (4 points] Under the assumption above, what is the maximum velocity and acceleration of the object?

Answer 1

Using conservation of energy:- we get the relation for velocity ,since we have to find maximum velocity x will be equal to a and formula for max velocity is aw.

a) हम gi T b ) a = M²=k 1 mv²= Ika2 Time period sT = 28 Angular, 3.14 rad/s frequency T= at Kami² & mass, m= 4 kg К: чп? - = 39.43 N/m c) Amplitude Total Energy Ika? IX x 41 ? x 400X10-4 8 772 x 10-2 Using conervation of Energy For Vmax when est amax Vmax 20x102x IT? X a 1) 0.788 J d ) a K 20x 10-2 x (1 -0.628 m/s Max. acc. = cura T² x 20 x 10-2 1.977 m/s²