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GROUP Assignment. A block of mass m = 680 grams is attached to a spring whose...

GROUP Assignment. A block of mass m = 680 grams is attached to a spring whose spring constant k is 65 N/m. The block is pulled a distance x = 11 cm from its equilibrium position at x = 0 on a frictionless surface and released from rest at t = 0 s. (a) What are the angular frequency ω, frequency f, and period T of the resulting motion? (b) What is the amplitude A, the maximum speed v_max, and the maximum acceleration a_max of the block?

Expert Solution

Given : mss of block = 680 g = 0.68 Kg force constant = 65 N / m

The displacement , x = 11 cm = 0.11 m

( a ) According to Hooke's Law F = -kx

ma = -Kx since F = ma according to newton's second law

a = - K /m . x

Angular velocity , = K /m = 65 / 0.68 = 9.8 rad / s

the frequency , f = / 2 = 9.8 / ( 2 x 3.14 ) = 1.6 H_z

The time period , T = 1 /f = 1 / 1.6 = 0.64 s

( b ) As the displacement 11 cm is the maximum displacement the maximum amplitude is 11 cm.

i.e A = 11 cm.

The maximum speed , V_max = x_max

= 9.8 rad /s x 11 cm = 107.8 cm /s =1.1 m/s

The maximum acceleration = ² x_max

= 9.8 x9.8 x 11 = 1056.44 cm /s = 10.5644 m/ s = 11 m/s

genius_generous answered 1 year ago

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