At time t=0.0 s, a horizontal spring with the spring constant of 5.0 N/m is stre

Question

At time t=0.0 s, a horizontal spring with the spring constant of 5.0 N/m is stretched by 4.0 cm in the positive direction; a small block with the mass of 20.0 g is attached to the free end of the spring, and then released from rest. It is moving along a frictionless horizontal surface.

1. Determine (i) amplitude A and (ii) angular frequency, and (iii) period of this SHM.

2. What is the maximal speed that the block will have?

3. What is the location of the block (relative to the equilibrium) when it is moving at 0.10 m/s in the negative direction?

Explanation / Answer

Here ,

1)

as the spring is intiially stretched by 4 cm ,

the amplitude of is 4 c m

b)

angular frequency , w = sqrt(k/m)

w = sqrt(5/0.020)

w = 15.81 rad/s

c)period , T = 2pi/w

T = 2pi/15.81

T = 0.397 s

the period of SHM is 0.397 s

2)

let the maximum speed is v

using conservation of energy

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

5 * 0.04^2 = 0.5 * 0.020 * v^2

v = 0.283 m/s

maximum speed of the block is 0.283 m/s

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