A mass, m = 0.50 kg, is attached to a horizontal spring of spring constant, k =

Question

A mass, m = 0.50 kg, is attached to a horizontal spring of spring constant, k = 200 N/m. The mass is given an initial displacement of 0.015 m and an initial velocity of +0.40 m/s. a) Find the period, amplitude, and phase angle of the motion. b) Write equations for the displacement, velocity and accelerations as a function of time. A mass oscillating in simple harmonic motion starts at x = A and has a period of T. At what time, as a fraction of T, does the object first pass through x = (1/2)A? An object on a spring oscillates with a period of 0.80 s and an amplitude of 10 cm. At t = 0 s, it is 5.0 cm to the left of equilibrium and moving to the left. What are its position and direction of motion at t = 2.0 s? An 83 kg student hangs from a bungee cord with a spring constant of 270 N/m. The student is pulled down to a point where the cord is 5.0 m longer than its unstretched length, then released. Where is the student, and what is his velocity 2.0 s later? Question1

Explanation / Answer

Question 1

let the equation of motion of block be

x=Asin(wt+B)

v=dx/dt=Awcos(wt+B)

at t=0 ,x=0.015m,v=0.4 m/s

sin(B)=0.015

B=0.015

w=sqrt(K/m)=20 rad/s

Awcos(B)=0..4

we got

A=0.02 m

(b) equation

x=0.02sin(20t+0.015)

v=0.4cos(20t+0.015)

a=dv/dt=-0.8sin(20t+0.015)

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