# Two blocks of masses #m_1# and #m_2# are connected with a light spring of force constant #K# and whole system is kept on a frictionless horizontal surface the masses are applied forces #f_1# and #f_2# respectively?

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At any time the blocks have accelerations a. The value of spring force is?

At any time the blocks have accelerations a. The value of spring force is?

See below.

If the acceleration is the same then

adding both equations

and now subtracting

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The system will undergo oscillatory motion due to the forces applied by ( f_1 ) and ( f_2 ) respectively, and the restoring force from the spring. The motion will depend on the masses ( m_1 ) and ( m_2 ), the force constants of the spring ( K ), and the magnitudes and directions of ( f_1 ) and ( f_2 ). The specific behavior can be analyzed using principles of classical mechanics and Newton's laws of motion.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- If the length of a #15 cm# spring increases to #28 cm# when a #2 kg# weight is hanging from it, what is the spring's constant?
- A box with an initial speed of #4 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #5/4 # and an incline of #(3 pi )/4 #. How far along the ramp will the box go?
- An object with a mass of # 12 kg# is lying on a surface and is compressing a horizontal spring by #40 cm#. If the spring's constant is # 4 (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?
- An object with a mass of #6 kg# is on a surface with a kinetic friction coefficient of # 8 #. How much force is necessary to accelerate the object horizontally at # 9 m/s^2#?
- An object with a mass of # 18 kg# is lying on a surface and is compressing a horizontal spring by #60 cm#. If the spring's constant is # 4 (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?

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