Question

Saved Help 2 attempts left Cbeck o my work Round to two decimal places if necessary A spring is stretehed 10 centimeters by a 15 N weight. The weight is then pulled down an additional 4 centimeters and released. Neglect damping. Find an equation for the position of the spring at any time t. u(t)-0.07cos (t)

Answer 1

Given that weight w = 15 N s = 10 cm = 0.01 m x = 4 cm = 0.04 m Mass = w/g = 15/9.8 m = 75/49 k = w/x = 15/0.04 k = 375 equation of the system is mx^�� + kx = 0 75/49 x^�� + 375 x = 0 Auxillary equation is 75/49 x^2 + 375 x = 0 r(75/49 x + 375) = 0 \r\n 75/49 r + 375 = 0 75/49 r = -375 r = -375 times 49/75 r = -245 r = 0, -245 Roots real and distinct then x(t) = c_1 e^r_1 x + c_2 e^r_2 x u(t) = c_1 e^0 x + c_2 e^-245 x u(t) = c_1 + c_2 e^-245 x