Question

A block-spring system consists of a spring with constant k = 445 N/m attached to a 2.25 kg block on a frictionless surface. The block is pulled 4.10 cm from equilibrium and released from rest. For the resulting oscillation, find the amplitude, angular frequency, frequency, and period. What is the maximum value of the block's velocity and acceleration?

Answer 1

here, k = 445 N/m, m= 2.25 kg, and is displaced 4.10 cm from equilibrium and released from rest. So, amplitude of the resulting oscillation is 4.10 cm= 0.041m

Now, using the relations for simple harmonic motion;

angular frequency is given by w= (k/m)^1/2= (445/2.25)^1/2= 14.06/s

Also, Frequency= w/2π= 14.06/2*3.14= 2.24 Hz

Also, period= 2π(m/k)^1/2= 2*3.14*(2.25/445)^1/2= 0.4467s

Maximum velocity= Amplitude*angular frequency= 0.041*14.06= 0.576m/s

Maximum acceleration= Amplitude*angular frequency^2= 0.041*14.06^2= 8.1m/s^2

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