(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A 5kg sphere is connected to a thin massless but rigid rod of length L=1.3 m to form a simple pendulum. The rod is connected to a nearby vertical wall by a spring with a spring constant k= 75N/m, connected to it at a distance h=1.1 m below the pivot point of the pendulum. What is the angular frequency (in rad/s) of the system for small amplitude oscillations.

2. Relevant equations

[tex]\alpha[/tex] = [tex]\omega[/tex]^{2}*[tex]\theta[/tex]

I=m*r^{2}

Torque=f*d*sin[tex]\theta[/tex]

or small oscillations, sin[tex]\theta[/tex]=[tex]\theta[/tex] and cos[tex]\theta[/tex]=1

3. The attempt at a solution

sum the torque and set them equal to [tex]\alpha[/tex]I

gravitational torque= Lmg[tex]\theta[/tex]

if theta is the angle between the rod and its equilibrium position, the angle of the spring torque is (theta + [tex]\pi[/tex]/2), so the spring torque is

f*d*sin(theta + [tex]\pi[/tex]/2). The force is k*[tex]\Delta[/tex]x, or h*sin(theta + [tex]\pi[/tex]/2) and the distance is h, giving

torque from spring =k*h^{2}*sin[tex]\theta[/tex]*sin(theta + [tex]\pi[/tex]/2)

or k*h^{2}*[tex]\theta[/tex]*(theta + [tex]\pi[/tex]/2)

My final equation is

mL^{2}[tex]\omega[/tex]^{2}tex]\theta[/tex] = Lmg[tex]\theta[/tex] + k*h^{2}*[tex]\theta[/tex]*(theta + [tex]\pi[/tex]/2)

The problem is that this gives me a [tex]\omega[/tex] that is dependant on [tex]\theta[/tex], which isn't possible. It should be constant. Can someone please tell me where I'm going wrong?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Pendulum with horizontal spring

**Physics Forums | Science Articles, Homework Help, Discussion**