Question

A block with a mass of 2.00 kg is attached to a spring, undergoing a horizontal simple harmonic motion with a period of 1.26 s. The initial speed of the block is 1.20 m/s when the spring is stretched by 25.0 cm. Let x = 0 at the equilibrium position. Ignore friction.

a)Find the spring constant.

b)Find the total energy of this object.

c)Find the maximum displacement of the motion.

d)Find the maximum speed.

e)For the block, at what position x is the speed a minimum? At what position x is the acceleration a minimum (in magnitude)? Show your answers of x as numerical values. You don’t have to explain in this part.

Answer 1

A) Time Period is given by,

Where "m" is the mass and "k" is the spring constant.

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B) Total energy = Kinetic energy + Potential energy

Kinetic energy is given by,

Spring potential energy is given by ,

When spring is streched at 25cm velocity = 1.20m/s

Calculating total energy at 25cm

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C) Total energy is always a constant.

At maximum displacement, velocity is zero.

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D) Again use conservation of energy

Maximum velocity is at displacement =0

At , x=0

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e) Speed is minimum when displacement is maximum

x= 34.7 cm is point of minimum speed. (34.7 cm in both direction with respect to 0)

Acceleration is minimum where displacement is minimum

x=0 cm is the point of minimum acceleration.

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