An oscillating block-spring system has a mechanical energy of 1.00 J, an amplitude of 11.2 cm, and a maximum speed of 1.08 m/s.
(a) Find the spring constant.
___ N/m
(b) Find the mass of the block.
___ kg
(c) Find the frequency of oscillation.
___ Hz
.. im having difficulty finding the spring constant and the mass.
my answer for (c) is 1.51 Hz
i tried to find the velocity w through this equation with the maximum speed given:
v = wx
1.08 m/s = (w)(0.112m)
w = 9.64 rad/s
and to find the frequency:
f = w/2pi
f = (9.64 rad/s)/(2pi)
f = 1.51 Hz
.. and now im stuck.
the angular frequency has the mass m and the spring constant k that i need.
w = sqrt(k/m) = 9.64 rad/s
please help me find the mass & the spring constant?! thanks :)
This is about as messed up as possible. First, you said you tried to find velocity w with v=wx. Where did you get that?
To start, you know max displacement A.
Max PE= 1/2 k A^2
But you know the max PE (max energy), so solve for k.
Then, knowing the max KE (msx energy), solve for mass from 1/2 mv^2 equaling max energy.
Finally, maxvelocity= wA, solve for w, angular frequency.
http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html