- #1
toothpaste666
- 516
- 20
Homework Statement
A mass,m, hangs from a string and swings with a frequency of 0.8 Hz with
a maximum
displacement of 0.1 rad. The equation of motion is given by
x=Acos(ωt).
A) What is the length of the string?
B) What is the maximum displacement of the mass in meters?
C) What is the velocity of the mass as a function of time? Leave the answer as a function of m,g,L, and θmax
(Hint: Take the derivative of the equation of motion).
D)
What is the restoring force acting on the mass as a function of time? Leave the answer as a function of m,g,L, and θmax
(Hint: Find the acceleration)
Homework Equations
ω=sqrt(g/l)
ω=2pif
The Attempt at a Solution
for part a) ω = 2pif and ω = sqrt(g/l) (since this is a simple pendulum)
so
2pif=sqrt(g/l)
or
l=g/(4pi^2f^2) = 9.8/(4pi^2(.8)^2) = .39m
for part b i can't figure out how to get .1 rads into meters. this is my attempt so far
(.1 rad) (cycle/2pi rad) (second/.8cycle) = .02 seconds
for part c take the derivativedx/dt = d/dt(Acos(sqrt(g/l)t))
v = -Asin(sqrt(g/l)t)(sqrt(g/l)
im guessing the theta max that the question wants v defined in terms of will be part of Apart d
a = dv/dt = d/dt(-Asin(sqrt(g/l)t)(sqrt(g/l))
= -Acos(sqrt(g/l)t)(g/l)
then use F = ma = -kx
m * -Acos(sqrt(g/l)t)(g/l)
any feedback?