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
To find the spring constant and the mass in the given system, we can use the equations for mechanical energy, max potential energy, and max kinetic energy.
(a) Finding the spring constant (k):
The mechanical energy of the system is given as 1.00 J. The mechanical energy of a block-spring system is the sum of potential energy (PE) and kinetic energy (KE).
Total mechanical energy = PE + KE
We know that the max potential energy is 1/2 k A^2, where A is the amplitude of the oscillation.
So, we can set up the equation:
1.00 J = (1/2) k (0.112 m)^2
Solving this equation for k, we can find the spring constant.
(b) Finding the mass (m):
The maximum kinetic energy is also equal to the mechanical energy. It can be expressed as 1/2 m v^2, where v is the maximum speed of the block.
So we can set up the equation:
1.00 J = (1/2) m (1.08 m/s)^2
Solving this equation for m, we can find the mass of the block.
(c) Finding the frequency (f):
The frequency of oscillation can be calculated from the angular frequency (w) using the formula:
f = w / (2π)
Since we already have the angular frequency (w) as 9.64 rad/s, we can substitute it into the above formula to find the frequency.
Using the equations and solving for k, m, and f will provide the answers to the respective questions.