HELP PLEASE! I\'M STUCK! The motion of an undamped Mass-spring system is called
ID: 1265027 • Letter: H
Question
HELP PLEASE! I'M STUCK!
The motion of an undamped Mass-spring system is called harmonic oscillation. If a weight of 9.8 Newtons stretches a certain spring by 0.14m(g=9.8m/s^2, the unit of the spring constant k is Newtons/m)
a) Find the mass m of the weight
b) Find the spring constant k
c) Write a model for the undamped harmoic oscilation (write an ODE)
d) Find two real valued basic solutions for the ODE and use Wronskian to show that these two basic solutions are linearly dependent.
e) Write down the real valued general solution of the model
Explanation / Answer
A. Use the formula for force F = mg = kx
where m is mass
g is gravity = 9.8 m/s^2
k is spring constant
x is compression
so
m = 9.8/9.8 = 1kg
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use mg = kx
K = 9.8/0.14
k = 70 N/m
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