In this lesson, we will learn how to calculate the instantaneous position, velocity, acceleration, and energy of simple harmonic spring oscillators.

Q1:

A type of clock keeps time by the oscillation of a small object bouncing on a spring. What force constant of a spring is needed to produce a period of 0.370 s for an object of mass 0.0210 kg?

Q2:

Consider a block of mass 0.200 kg attached to a spring of spring constant 100 N/m. The block is placed on a frictionless table, and the other end of the spring is attached to the wall so that the spring is level with the table. The block is then pushed in so that the spring is compressed by 10.0 cm.

Find the speed of the block as it crosses the point where the spring is not stretched.

Find the speed of the block as it crosses the point 5.00 cm to the left of the point where the spring is not stretched.

Find the speed of the block as it crosses the point 5.00 cm to the right of the point where the spring is not stretched.

Q3:

A spring with a spring constant of 127 N/m, which can be stretched or compressed, is placed on a frictionless horizontal table. An object of mass 9.77 kg is attached to one end of the spring and the other end is anchored to a wall at one end of the table. The equilibrium position of the object is marked as zero. A student moves the object 6.2 cm from its equilibrium position, extending the spring, and then releases the mass. Consider displacement in the direction that extends the spring to be positive-valued.

Find the position of the object at π‘ = 4 . 0 s.

Find the velocity of the object at π‘ = 4 . 0 s.

Find the acceleration of the object at π‘ = 4 . 0 s.

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