A 100 gram block, attached to the end of an ideal spring (horizontal) with force

Question

A 100 gram block, attached to the end of an ideal spring (horizontal) with force constant k = 100 N/m, undergoes simple harmonic motion with a maximum displacement of 5.0 cm from the relaxed position. Ignore any friction or air resistance. Compute the speed of the block at position. Compute the acceleration of the block at position 5 Compute the linear frequency of the oscillations At which positions the spring force on the block is the maximum? At which positions the speed of the block is Zero? How much lime does it take the block to travel from position O to the position 2 What is the mechanical energy of the block at the position O? On the picture, the positions # 1 and 5 correspond to the extreme positions, x = 5 cm and x = -5 cm, while the position 3 corresponds to the relaxed position of the spring, x = 0. Position 2 and 4 are intermediate.

Explanation / Answer

here,

mass , m = 0.1 kg

k = 100 N/m

Amplitude , A = 5 cm = 0.05 m

b)

let the speed of block at 3 be v

using conservation of energy

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

0.1 * v^2 = 100 * 0.05^2

v = 1.58 m/s

the speed at position 3 is 1.58 m/s

c)

the accelration of the block at 5 , a = F/m

a = k* A/m

a = 100 * 0.05 /0.1

a = 50 m/s^2

d)

the linear frequency of oscillation , f = 1/2pi * sqrt(k/m)

f = 1/2pi * sqrt(100/0.1)

f= 5.04 Hz

e)

at position 1 and 5 , the force on the block is maximum

f)

the speed of block is zero at maximum elongation i.e 1 and 5

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