A mass on a frictionless table is attached to a spring that stretches horizontal

Question

A mass on a frictionless table is attached to a spring that stretches horizontally. The mass oscillates between the 10.0 cm mark and the 60.0 cm mark on a meter stick lying on the table. The mass completes 10.0 oscillations in 33.0 s. What are the: period frequency amplitude maximum speed of the mass? A 1.00 kg block is attached to a spring with a spring constant of 16.0 N/m. While the block is sitting at rest, a student hits it with a hammer and almost instantly give it a speed of 40.0 cm/s. What are: The amplitude of the subsequent oscillations? The block's speed at x = 1/2 A? Hint: There is a potential energy at this point!

Explanation / Answer

1]

b] Frequency, f= n/T= 10/33= 0.303 Hz

a] Period, T= 1/f= 3.3s

c] Amplitude, A= 60cm-10cm=50cm=0.50m

d] Maximum speed, Vmax=?

wmax=2*pe*f= 2*3.14*0.303 =1.90 rad/s

vmax= A*wmax= 0.50m*1.90 rad/s= 0.95m/s

2] a]

Applying conservation of energy

Pe block= Ke spring

1/2mv2= 1/2kA2

1/2*1* 0.402= 1/2*16*A2

A=0.1m

Amplitude of the subsequent oscillation is 0.1m

b]

At x=1/2A=1/2*0.1= 0.05m

Pe= 1/2kx2= 1/2*16*0.052=0.02J

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