Derive the equation of motion of the spring-mass system given below. show and mark your derivation step by step. missing steps will result in losing points. use the assumptions sin(θ) = θ and cos(θ) = 1.

Ö + θ ( (k/m) + (g/l)) = 0

Step-by-step explanation:

Use the FBD attached:

Apply Newtons 2 nd Law in tangential direction:

Sum ( Ft ) = m*a

Sum of all tangential forces is:

m*g*sin(θ) + k*l*sin(θ)*cos(θ) = - m*l*Ö

Using small angle approximations:

sin (θ) = θ

cos (θ) = 1

Ö = angular acceleration.

m*g*θ + k*l*θ = -m*l*Ö

Ö + θ ( (k/m) + (g/l)) = 0

$450

step-by-step explanation:

first, you have to multiply 150x2=300

next, you have to add 150+300= 450