A block-spring system consists of a spring with constant k 445 N/m attached to a

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 4.90 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? HINT (a) amplitude (in m) (b) angular frequency (in rad/s) 4.9 rad/s (c) frequency (in Hz) Hz (d) period (in s) (e) maximum velocity (in m/s) m/s maximum acceleration (in m/s2) 4.0 (f) m/s2

Explanation / Answer

Given

spring constant k = 445 N /m

mass of block is m = 2.25 kg

the displacement from equilibrium positionis x = 4.90 cm = 0.049 m

and making oscillations when it is released from rest due to restorin force in the spring

a) the amplitude is the maximum displacement from mean position here A = 0.049 m

b) the angular frequency W = sqrt(k/m) = sqrt(445/2.25) rad /s = 14.06 rad/s

c) frequency f is , W = 2pi*f ===> f = W/2pi = 14.06/(2pi) Hz = 2.24 Hz

d) period is T = 1/f = 1/2.24  

e) maximum velocity will be at equilibrium position

that is U = k.e

0.5*k*A^2 = 0.*m*v^2

v= A*sqrt(k/m)

V = 0.049 sqrt(445/2.25) m/s

V = 0.6891 m/s

f) maximum acceleration is  

kx = ma

a = (k/m)(x) = (445/2.25)(0.049) m/s2

a = 9.69 m/s2

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