Question

2. You will solve the following problem twice, first using kinematics and second using the ideas of conservation of energy: A mass is attached to a spring with a spring constant of k=11 N/m. The motion of the mass can be described by the equation r(t) = 35 cos (1.210 t), where x(t) is cm. You want to figure out how fast the mass is moving at x = 28 cm. a. Find a solution using the kinematic relationship, v(t) = X(t). b. Find a solution using the principle of conservation of energy: E = KE + U

Answer 1

Acerrding to the questim, motion of mass (4= 35eos (1.27t) At x=28 em, then from ea o 28-35 col.2 them 1.200 = cost) = 36.97 libee Vordr -35 x 1.2 Sir' 1.2T) UUUUUUUUUUUU y = - 1:32 Sin (36.87) = -0.8m's 6 We know that, 6 = EU since Total Energy = kinetic energy+ potential energy = KA2 = amin- I ka? & KA_Kx²=v² v= I (A²x3* v=w San N2IT JE357-10,2872 1 = 0.8 m/s/

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