 A particle is undergoing simple harmonic motion with the equation 6 cos pi by 4t plus 5 where x is measured in meters and time in seconds. Here we can see the motion of the particle, the SHM of the particle. Initially the particle is 3 meters to the left of equilibrium position and we need to figure out the value of 5. Alright, so let's try to work this out. We know the position of the particle at time t equals to 0 because it's initially, so time t equals to 0, we know that x is, this is equal to minus 3 meters because it is to the left of the equilibrium which is towards the negative side. So let's try to put these values into the equation. We have x of t, this is equal to 6 cos pi by 4t plus 5. So when t is 0, x becomes 3, so this becomes minus 3, this is equal to 6 cos pi t is 0. Now this gives us, this gives cos pi equals to minus 1 by 2. Let's try to recall cos pi was 1 by 2, cos pi was 1 by 2 when 5, cos pi was 1 by 2 when 5 was 60 right or pi by 3, this is when 5 was 5 by 3. And we need cos 5 to be equal to minus 1 by 2. Let's recall one identity. So when we wrote cos of pi minus x, this became minus cos x. So if we wrote cos of pi minus pi by 3, this will become minus cos pi by 3 or minus 1 by 2 which is what we need. So when we work this out, this becomes cos, this becomes cos of 2 pi by 3 which is really equal to minus 1 by 2. So 5 in this case, this is 2 pi by 3.