Solving for Spring Constant: Displacement and Time Relationship

[Holly3.9]

Homework Statement

The graph of displacement versus time for a small mass at the end of a spring is shown. At t = 0, x = 0.43 cm. (a) If m = 14.3 g, find the spring constant, k. (b) Write the equation for displacement x as a function of time.

Homework Equations

f = (1/2pi) * SQRT (k/m)
f = 1/Period = 1/ 0.69 sec = 1.45 cycles/sec
SQRT (k/m) = 2 * pi * f

k = m * (2 * pi * f )^2

k = 0.0143 kg * (2 * pi * 1.45 cycles/sec
)^2

The Attempt at a Solution

1.19 N/m

 

[Holly3.9]

graph : http://www.webassign.net/userimages/mowat@ncsu/FG14_029.JPG

SORRY!

 

[rl.bhat]

Your k value is correct.
The general equation of oscillation is
x = x0*sin(ωt + φ)
When t = 0, x = x0*sin(φ)
Put the values of the x and xo and find the value of φ. Then write the general equation.