A 3kg block is attached to a massless spring and oscillates back and forth with

Question

A 3kg block is attached to a massless spring and oscillates back and forth with simple harmonic motion according to the equation x(t)=4cos(5t), where x is in meters And t is in seconds. What is the spring constant of the spring? A)43N/m B)12N/m C)75N/m D)20N/m E)60N/m What is the maximum velocity of the block? A)5m/s B)20m/s C)70m/s D)100m/s E)150m/s A 3kg block is attached to a massless spring and oscillates back and forth with simple harmonic motion according to the equation x(t)=4cos(5t), where x is in meters And t is in seconds. What is the spring constant of the spring? A)43N/m B)12N/m C)75N/m D)20N/m E)60N/m What is the maximum velocity of the block? A)5m/s B)20m/s C)70m/s D)100m/s E)150m/s A 3kg block is attached to a massless spring and oscillates back and forth with simple harmonic motion according to the equation x(t)=4cos(5t), where x is in meters And t is in seconds. What is the spring constant of the spring? A)43N/m B)12N/m C)75N/m D)20N/m E)60N/m What is the maximum velocity of the block? A)5m/s B)20m/s C)70m/s D)100m/s E)150m/s What is the spring constant of the spring? A)43N/m B)12N/m C)75N/m D)20N/m E)60N/m What is the maximum velocity of the block? A)5m/s B)20m/s C)70m/s D)100m/s E)150m/s

Explanation / Answer

First question:

m=3Kg

x(t)=4*cos(5t)

Comparing with: x(t)=A*cos(wt), then:

Amplitude A=4 m

Angular velocity: w=5 rad/sec

So:

w=sqrt(k/m)

k=m*w^2

k=3*5^2

= 75 N/m (C) is correct

Second question:

Vmax=A*w

=4*5

=20 m/sec (B) is correct

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