Question

the angular velocity of a mass attached to a spring is denoted by​

Answer 1

Answer:

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Explanation:

The displacement equation for an oscillating mass is given by:

x=Acos(ωt+θ)

Velcoity, v=dx/dt=−Aωsin(ωt+θ)

At t=0,x=x  

0

​

 

x  

0

​

=Acosθ=x  

0

​

  ...(i)

and, dx/dt=−v  

0

​

=Aωsinθ

Asinθ=v  

0

​

/ω  ...(ii)

Squaring and adding equations (i) and (ii), we get:

A  

2

(cos  

2

θ+sin  

2

θ)=x  

0

2

​

+(  

ω  

2

 

v  

0

2

​

 

​

)

∴A=  

x  

0

2

​

+(  

ω

v  

0

​

 

​

)  

2

 

​

 

Therefore, the amplitude of the resulting oscillation is (x  

0

2

​

+(  

ω

v  

0

​

 

​

)  

2

)  

2

1

​

 

.