Acos (your equation in x - ( t + ) should 5 points) The function X (t)-0.4m Cos

Question

Acos (your equation in x - ( t + ) should 5 points) The function X (t)-0.4m Cos [(4 rad/s) t + (21) rad] gives the simple harmonic motion of a body attached to a spring. The total energy of the system is E- 500 J. At exactly t 15 s what are the a) velocity b) acceleration c) phase of the motion, d) Find the spring constant Note: The block is momentarily at rest at its maximum displacement. 4 points) A car of mass 980 kg oscillates up and down at a frequency of 1.8Hz with an amplitude of 2.6cm when the driver gets out and no one is . the car a) What is the period of oscillations, in seconds? b) How large is the spring constant associated with the oscillations? c) How much energy is associated with the oscillations? d) If five people with a total mass of 330kg get in the car, what would be the oscillation frequency? 4 points)

Explanation / Answer

x(t)=0.4cos[(4)t+(2/3)]

Compare this eqn with,

x(t)=Acos(wt+)

We get,

A=0.4m, w=4, =2/3, t=1.5s

a)v=dx/dt = -Awsin(wt+)=-0.4*4*sin[(4)*1.5+(2/3)] = -4.35 m/s

b) a=dv/dt = -Aw^2cos(wt+)= -0.4*(4)^2*sin[(4)*1.5+(2/3)] =-54.7 m/s^2

c) Phase= =2/3

d)

E=1/2kA^2

500=1/2*k*0.4^2

k= 6250 N/m

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