A 332g mass is attached to a spring and undergoes simple har

A 332-g mass is attached to a spring and undergoes simple harmonic motion. Its maximum acceleration is 16.6 m/s2 , and its maximum speed is 1.75 m/s. What is the angular frequency? I honestly have no idea how to get w without k.

Solution

According to the question provided we need to find the angular frequency.

A(max) = 16.6 m/s^2

force =ma = ( 0.332 ) * ( 16.6 ) = 5.5112 N = kA

energy = 1/2*m*v^2 = 0.5*0.332*(1.75)^2 = 0.508375
spring (p.e) = 1/2*k*A^2

0.5kA^2 = 0.508375

2.7556 A = 0.508375

A = 0.184487 m

K = 5.5112 N / 0.184487 m = 29.87310 N/m

angular frequency =(k/m) = (29.87310/0.332) = 9.485738 ==================ANSWER)