# Find Amplitude and Frequency

1. Nov 9, 2008

### dsptl

* A 200g block attached to a horizontal spring is oscillating with an amplitude of 3 cm and a frequency of 2 Hz. Just as it passes through the equilibrium point a shalock so trp blow exerts a force impulse on the that the speed of the block is increased by .5m/s. What are the new a) frequency and b) amplitude?

My Attempt:

total energy of the mass moving with amplitude A and oscillating with frequency f will be
E = mA^2ω^2 / 2

where ω = 2πf
f = frequancy of oscillation
A = amplitude of oscillation .
at the mean postion the total eneregy will be in kinetic energy form
E = mv^2 / 2
v =velocity of the mass at equalibrium
if 0.5m/sec is added to velocity

Now the new total eneryg
E' = m*(v + 0.5)^2 / 2 .
m = mass of the block
E' = mA'^2 ω^2 / 2
the frequancy remains constanat
and the amplidue to of the new oscillation changes
ω = 2E' / mA'^2

but at the end I am left with 2 unknown and i am not to solve this

2. Nov 9, 2008

### alphysicist

Hi dsptl,

That's right; so what is the speed of the mass at the equilibrium point before the force impulse add the 0.5m/s? Then you will be able to find the value of the energy after the force impulse. What do you get?

3. Nov 9, 2008

### dsptl

total energy of the mass moving with amplitude A and oscillating with frequency f will be
E = mA^2ω^2 / 2 = (.2)(.03)^2(4pi)^2 / 2 = .0142J

where ω = 2πf
f = frequancy of oscillation
A = amplitude of oscillation .

at the mean postion the total eneregy will be in kinetic energy form
E = mv^2 / 2
.0142 = .2 v^2 /2

v = .377m/s

v =velocity of the mass at equalibrium
if 0.5m/sec is added to velocity = .377m/s + .5m/s = .877m/s

Is this right till this point? after this point I have no idea what to do....

Now the new total eneryg
E' = m*(v + 0.5)^2 / 2 .
m = mass of the block
E' = mA'^2 ω^2 / 2
the frequancy remains constanat
and the amplidue to of the new oscillation changes

.

4. Nov 9, 2008

### alphysicist

Perhaps I'm not understanding what you're asking, but you now can solve for A', since you have everything else.