An object of unknown mass oscillates on the end of a spring wit period 8 s. A 10kg object is attached to the first object, changing te period to 12 s. What is the mass of the first object

Explanation:

Let the first object have a mass of M

And a period of T1=8sec

The second object has a mass 10kg and a period of T2=12 sec

It is know that,

The period of a spring-mass system is proportional to the square root of the mass and inversely proportional to the square root of the spring constant.

T=2π√(m/k)

Then the constant in this equation is the spring constant (k) and 2π, which does not change for the same material.

Then, make k subject of formulas

T²=4π²(m/k)

T²k=4π²m

Then, k/4π²=m/T²

So the k is directly proportional to m and inversely proportional to T²

M1/T1²=M2/T2²

Since, M1 is unknown, M2=10kg, T1=8sec and T2=12

Then,

M1/T1²=M2/T2²

M1/8²=10/12²

M1/64=0.06944

M1=0.06944×64

M1=4.444kg

The mass of the first object is 4.44kg

okay i have so many questions. but the big one here is: um wt..f is this mess? ?

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards