A mass of 0.40 kg is attached to a spring and set into oscillation on a horizont

Question

A mass of 0.40 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by x(t) = (0.20 m)cos[(20 rad/s)t]. Determine the following.

(a) amplitude of oscillation for the oscillating mass
m

(b) force constant for the spring
N/m

(c) position of the mass after it has been oscillating for one half a period
m

(d) position of the mass one-third of a period after it has been released
m

(e) time it takes the mass to get to the position x = ?0.10 m after it has been released

s

Explanation / Answer

mass , m=0.40 kg

x(t) = (0.20 m)cos[(20 rad/s)t]

compare with standard equation

x = A cos(wt)

a)
amplitude A =0.2 m

------------
b)

force consnt ,K = mw^2 = 0.4*20^2 = 160 N/m

-----------
c)

Time period , T = 2pi/w = 2pi/20 = 0.31415 sec

after half time peroid the position is

x = 0.20 cos(20*0.31415/2)

x = - 0.2 m

-----------
d)

one-third of a period after it has been released

x = 0.2 cos(20*0.31415/3)

x = -0.1 m

------------
e)

when x = - 0.10 m

-0.1 = 0.2 cos(20t)

time t = 0.104 sec
----------------

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.