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need help finding phase angle in SHM?
In a spring block system the mass of the block is 0.2kg and k=5N/m. The spring compresses by 6cm at time t=π/10s and has a velocity of -40cm/s. Find the equation of the displacement
I have trouble finding the phase angle.
1 Answer
- 6 years ago
From :k=mw^2 ,where w: angular velocity
=> w=5m/s
Since x^2 +(v/w)^2 = A^2 ,where x:displacement and A: amplitude
=> A= 10cm (change x and v to meters before calculating A)
The angle that the string have experienced SHM since the beginning (t=0) to t=pi/10 : (w)x(t)=pi/2
=> we have : (x1/A)^2 + (x2/A)^2 = 1 =>x1 when t=0 is 8 cm
Since v<0 when t =0 => The system is following the negative direction
Let a be the phase angle => a= arccos(8/10)= 36.87 degree
We have the equation : x=10cos(5t + 36.78 degree)