Question

A 3.70 kg object is attached to a spring and placed on frictionless, horizontal surface. A horizontal force of 19.0 N is required to hold the object at rest when it is pulled 0.200 m from its equilibrium position (the origin of the x axis). The object is now released from rest from this stretched position, and it subsequently undergoes simple harmonic oscillations (a) Find the force constant of the spring, N/m (b) Find the frequency of the oscillations Hz (c) Find the maximum speed of the object. my's (d) Where does this maximum speed occur? Xt m (e) Find the maximum acceleration of the object. m/s2 Where does the maximum acceleration occur? (9) Find the total energy of the oscillating system. (h) Find the speed of the object when its position is equal to one-third of the maximum value. m/s 0) Find the magnitude of the acceleration of the object when its position is equal to one-third of the maximum value. m/s?

Answer 1

(a) 19 K = 0.2 95 (b) Frequency, f= 2 - 6,28 3.7 (d) 1195) (0.2) – 1.905 Force constant, k= = 95.0 N/m 95.0 N/m 0.807 HZS f = 0.80686 Hz = (maximum speed, may= AW 7 Vmax= 0.2 / 4 = 0.2895 - 101 m/s maximum speed anders occurs at equilibrium position il at (@ maximum acceleration, amax amax = (R) A = 5.1351 m/s (f) maximum acceleration is at extreme positions. il at x= +0.200m (h) at x = A/3, V= wfax = w JA - Alla = AW = Aw/s/a =) = 0,24 asx ſela = v=0.955 m/s w (4/3) => a=1.71 m/s² x-m . 2 A (ه) 95% 0.2 3.7 - amax = 5.14 m/s E = IKA 2 2 (8) at x = A/ Alz, a= 2