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dimaraw [331]
3 years ago
12

Derive the equation of motion of the spring-mass system given below. Please 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.

Mathematics
1 answer:
Arte-miy333 [17]3 years ago
5 0

Answer:

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

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